Subjects -> MATHEMATICS (Total: 1106 journals)
    - APPLIED MATHEMATICS (88 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (815 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (25 journals)
    - PROBABILITIES AND MATH STATISTICS (110 journals)

MATHEMATICS (815 journals)            First | 1 2 3 4 5     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Computational Physics     Hybrid Journal   (Followers: 70)
Journal of Computational Physics : X     Open Access   (Followers: 1)
Journal of Computer Engineering, System and Science (CESS)     Open Access  
Journal of Contemporary Mathematical Analysis     Hybrid Journal  
Journal of Cryptology     Hybrid Journal   (Followers: 3)
Journal of Difference Equations and Applications     Hybrid Journal  
Journal of Differential Equations     Full-text available via subscription   (Followers: 1)
Journal of Discrete Algorithms     Hybrid Journal   (Followers: 4)
Journal of Discrete Mathematics     Open Access   (Followers: 1)
Journal of Dynamics and Differential Equations     Hybrid Journal  
Journal of Engineering Mathematics     Hybrid Journal   (Followers: 2)
Journal of Evolution Equations     Hybrid Journal  
Journal of Experimental Algorithmics     Full-text available via subscription   (Followers: 1)
Journal of Flood Risk Management     Hybrid Journal   (Followers: 13)
Journal of Formalized Reasoning     Open Access   (Followers: 2)
Journal of Function Spaces     Open Access  
Journal of Functional Analysis     Full-text available via subscription   (Followers: 2)
Journal of Geochemical Exploration     Hybrid Journal   (Followers: 1)
Journal of Geological Research     Open Access   (Followers: 1)
Journal of Geovisualization and Spatial Analysis     Hybrid Journal  
Journal of Global Optimization     Hybrid Journal   (Followers: 7)
Journal of Global Research in Mathematical Archives     Open Access   (Followers: 1)
Journal of Group Theory     Hybrid Journal   (Followers: 2)
Journal of Homotopy and Related Structures     Hybrid Journal  
Journal of Honai Math     Open Access  
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Journal of Hyperbolic Differential Equations     Hybrid Journal  
Journal of Indian Council of Philosophical Research     Hybrid Journal  
Journal of Industrial Mathematics     Open Access   (Followers: 2)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 2)
Journal of Integrable Systems     Open Access   (Followers: 1)
Journal of K-Theory     Full-text available via subscription  
Journal of Knot Theory and Its Ramifications     Hybrid Journal   (Followers: 1)
Journal of Kufa for Mathematics and Computer     Open Access   (Followers: 1)
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 7)
Journal of Logical and Algebraic Methods in Programming     Hybrid Journal  
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 4)
Journal of Mathematical Analysis and Applications     Full-text available via subscription   (Followers: 4)
Journal of mathematical and computational science     Open Access   (Followers: 7)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 2)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 3)
Journal of Mathematical Cryptology     Hybrid Journal   (Followers: 1)
Journal of Mathematical Extension     Open Access   (Followers: 3)
Journal of Mathematical Finance     Open Access   (Followers: 9)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 3)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 1)
Journal of Mathematical Neuroscience     Open Access   (Followers: 10)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 8)
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 2)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 2)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access   (Followers: 6)
Journal of Metallurgy     Open Access   (Followers: 7)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access  
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 13)
Journal of Natural Sciences and Mathematics Research     Open Access  
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 1)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access  
Journal of Numerical Mathematics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access   (Followers: 4)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Problem Solving     Open Access   (Followers: 2)
Journal of Progressive Research in Mathematics     Open Access   (Followers: 1)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 4)
Journal of Quantitative Analysis in Sports     Hybrid Journal   (Followers: 8)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 18)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 1)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the European Mathematical Society     Full-text available via subscription   (Followers: 1)
Journal of the Indian Mathematical Society     Hybrid Journal   (Followers: 1)
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 2)
Journal of the Nigerian Mathematical Society     Open Access   (Followers: 1)
Journal of Theoretical and Applied Physics     Open Access   (Followers: 8)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 15)
Journal of Turbulence     Hybrid Journal   (Followers: 8)
Journal of Uncertainty Analysis and Applications     Open Access  
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 11)
Journal of Water and Land Development     Open Access   (Followers: 3)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 4)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access   (Followers: 4)
JURING (Journal for Research in Mathematics Learning)     Open Access   (Followers: 1)
Jurnal Ilmiah AdMathEdu     Open Access  
Jurnal Matematika     Open Access   (Followers: 1)
Jurnal Matematika Integratif     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access   (Followers: 3)
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access   (Followers: 5)
Le Matematiche     Open Access  
Learning and Teaching Mathematics     Full-text available via subscription   (Followers: 7)
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access   (Followers: 3)
Limits : Journal of Mathematics and Its Applications     Open Access   (Followers: 1)
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 22)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 8)
Lithuanian Mathematical Journal     Hybrid Journal  
LMS Journal of Computation and Mathematics     Free  
Lobachevskii Journal of Mathematics     Open Access  
Logic and Analysis     Hybrid Journal   (Followers: 1)
Logic Journal of the IGPL     Hybrid Journal   (Followers: 1)
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal  
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 2)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Matematika     Open Access  
Matematychni Studii     Open Access  
Mathematica Eterna     Open Access  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematica Slovaca     Hybrid Journal   (Followers: 1)
Mathematical and Computational Forestry & Natural-Resource Sciences     Free  
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 3)
Mathematical Journal of Interdisciplinary Sciences     Open Access   (Followers: 1)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 4)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling in Civil Engineering     Open Access   (Followers: 5)
Mathematical Modelling of Natural Phenomena     Full-text available via subscription   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 2)
Mathematical Models in Engineering     Open Access   (Followers: 6)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 3)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 13)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 3)
Mathematics and Statistics     Open Access   (Followers: 5)
Mathematics Education Forum Chitwan     Open Access   (Followers: 1)
Mathematics Education Journal     Open Access   (Followers: 1)
Mathematics Education Research Journal     Partially Free   (Followers: 17)
Mathematics in Science and Engineering     Full-text available via subscription  
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics of Quantum and Nano Technologies     Open Access  
Mathématiques et sciences humaines     Open Access   (Followers: 7)
Mathematische Annalen     Hybrid Journal   (Followers: 1)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 1)
MathLAB Journal     Open Access   (Followers: 4)
MATI : Mathematical Aspects of Topological Indeces     Open Access  
MATICS     Open Access   (Followers: 2)
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal  
Metascience     Hybrid Journal   (Followers: 1)
Milan Journal of Mathematics     Hybrid Journal  
Mitteilungen der DMV     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal   (Followers: 1)
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal   (Followers: 6)
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access   (Followers: 4)
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 3)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 1)
Nagoya Mathematical Journal     Hybrid Journal  
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal   (Followers: 1)
Natural Resource Modeling     Hybrid Journal   (Followers: 1)
New Mathematics and Natural Computation     Hybrid Journal  
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis : Theory, Methods & Applications     Hybrid Journal   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 2)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
Nonlinear Engineering     Open Access  
Nonlinear Oscillations     Hybrid Journal   (Followers: 1)

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Journal of Differential Equations
Journal Prestige (SJR): 2.525
Citation Impact (citeScore): 2
Number of Followers: 1  
 
  Full-text available via subscription Subscription journal
ISSN (Print) 0022-0396 - ISSN (Online) 1090-2732
Published by Elsevier Homepage  [3200 journals]
  • Markov shifts and topological entropy of families of homoclinic tangles
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Bráulio Garcia, Valentín MendozaAbstractThe existence of a homoclinic orbit in dynamical systems implies chaotic behaviour with positive entropy. In this work, we determine explicitly the Markov shifts associated to certain Smale horseshoe homoclinic orbits which allow us to compute a lower bound for the topological entropy that such a system can have. It is done associating a heteroclinic orbit which belongs to the same isotopy class and then determining the Markov partition of the dynamical core of an end periodic mapping.
       
  • Steady-state solutions of a reaction–diffusion system arising from
           intraguild predation and internal storage
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Hua Nie, Sze-Bi Hsu, Feng-Bin WangAbstractIntraguild predation is added to a mathematical model of competition between two species for a single nutrient with internal storage in the unstirred chemostat. At first, we established the sharp a priori estimates for nonnegative solutions of the system, which assure that all of nonnegative solutions belong to a special cone. The selection of this special cone enables us to apply the topological fixed point theorems in cones to establish the existence of positive solutions. Secondly, existence for positive steady state solutions of intraguild prey and intraguild predator is established in terms of the principal eigenvalues of associated nonlinear eigenvalue problems by means of the degree theory in the special cone. It turns out that positive steady state solutions exist when the associated principal eigenvalues are both negative or both positive.
       
  • A generalization of the Aubin–Lions–Simon compactness lemma for
           problems on moving domains
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Boris Muha, Sunčica ČanićAbstractThis work addresses an extension of the Aubin–Lions–Simon compactness result to generalized Bochner spaces L2(0,T;H(t)), where H(t) is a family of Hilbert spaces, parameterized by t. A compactness result of this type is needed in the study of the existence of weak solutions to nonlinear evolution problems governed by partial differential equations defined on moving domains. We identify the conditions on the regularity of the domain motion in time under which our extension of the Aubin–Lions–Simon compactness result holds. Concrete examples of the application of the compactness theorem are presented, including a classical problem for the incompressible, Navier–Stokes equations defined on a given non-cylindrical domain, and a class of fluid–structure interaction problems for the incompressible, Navier–Stokes equations, coupled to the elastodynamics of a Koiter shell. The compactness result presented in this manuscript is crucial in obtaining constructive existence proofs to nonlinear, moving boundary problems, using Rothe's method.
       
  • On the critical points of the flight return time function of perturbed
           closed orbits
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Adriana Buică, Jaume Giné, Maite GrauAbstractWe deal here with planar analytic systems x˙=X(x,ε) which are small perturbations of a period annulus. For each transversal section Σ to the unperturbed orbits we denote by TΣ(q,ε) the time needed by a perturbed orbit that starts from q∈Σ to return to Σ. We call this the flight return time function. We say that the closed orbit Γ of x˙=X(x,0) is a continuable critical orbit in a family of the form x˙=X(x,ε) if, for any q∈Γ and any Σ that passes through q, there exists qε∈Σ a critical point of TΣ(⋅,ε) such that qε→q as ε→0. In this work we study this new problem of continuability.In particular we prove that a simple critical periodic orbit of x˙=X(x,0) is a continuable critical orbit in any family of the form x˙=X(x,ε). We also give sufficient conditions for the existence of a continuable critical orbit of an isochronous center x˙=X(x,0).
       
  • Optimal lower eigenvalue estimates for Hodge-Laplacian and applications
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Qing Cui, Linlin SunAbstractWe consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold M¯. We first assume the pull back Weitzenböck operator of M¯ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of M¯ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when M¯ is the space form.
       
  • A refined convergence result in homogenization of second order parabolic
           systems
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Weisheng Niu, Yao XuAbstractWe derive the sharp O(ε) convergence rate in L2(0,T;Lq0(Ω)),q0=2d/(d−1) in periodic homogenization of second order parabolic systems with bounded measurable coefficients in Lipschitz cylinders. This extends the corresponding result for elliptic systems established in [20] to parabolic systems and improves the corresponding result in L2 settings derived in [7], [28] for second order parabolic systems with time-dependent coefficients.
       
  • Upper estimates for the number of periodic solutions to multi-dimensional
           systems
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Maoan Han, Hao Sun, Zalman BalanovAbstractThe maximal number of zeros of multi-dimensional real analytic maps with small parameter is studied by means of the multi-dimensional generalization of Rouché's theorem. The obtained result is applied to study the maximal number of periodic solutions to multi-dimensional differential systems. An application to a class of three-dimensional autonomous systems is given.
       
  • Blowup analysis for integral equations on bounded domains
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Qianqiao GuoAbstractConsider the integral equationfq−1(x)=∫Ωf(y) x−y n−αdy,f(x)>0,x∈Ω‾, where Ω⊂Rn is a smooth bounded domain. For 1
       
  • On the characterization of the controllability property for linear control
           systems on nonnilpotent, solvable three-dimensional Lie groups
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Víctor Ayala, Adriano Da SilvaAbstractIn this paper we show that a complete characterization of the controllability property for linear control system on three-dimensional solvable nonnilpotent Lie groups is possible by the LARC and the knowledge of the eigenvalues of the derivation associated with the drift of the system.
       
  • Fine regularity for elliptic and parabolic anisotropic Robin problems with
           variable exponents
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Maria-Magdalena Boureanu, Alejandro Vélez-SantiagoAbstractWe investigate a class of quasi-linear elliptic and parabolic anisotropic problems with variable exponents over a general class of bounded non-smooth domains, which may include non-Lipschitz domains, such as domains with fractal boundary and rough domains. We obtain solvability and global regularity results for both the elliptic and parabolic Robin problem. Some a priori estimates, as well as fine properties for the corresponding nonlinear semigroups, are established. As a consequence, we generalize the global regularity theory for the Robin problem over non-smooth domains by extending it for the first time to the variable exponent case, and furthermore, to the anisotropic variable exponent case.
       
  • Vanishing viscosity limit of short wave–long wave interactions in
           planar magnetohydrodynamics
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Daniel R. MarroquinAbstractWe study several mathematical aspects of a system of equations modelling the interaction between short waves, described by a nonlinear Schrödinger equation, and long waves, described by the equations of magnetohydrodynamics for a compressible, heat conductive fluid. The system in question models an aurora-type phenomenon, where a short wave propagates along the streamlines of a magnetohydrodynamic medium. We focus on the one dimensional (planar) version of the model and address the problem of well posedness as well as convergence of the sequence of solutions as the bulk viscosity tends to zero together with some other interaction parameters, to a solution of the limit decoupled system involving the compressible Euler equations and a nonlinear Schrödinger equation. The vanishing viscosity limit serves to justify the SW–LW interactions in the limit equations as, in this setting, the SW–LW interactions cannot be defined in a straightforward way, due to the possible occurrence of vacuum.
       
  • Phase portraits of piecewise linear continuous differential systems with
           two zones separated by a straight line
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Shimin Li, Jaume LlibreAbstractThis paper provides the classification of the phase portraits in the Poincaré disc of all piecewise linear continuous differential systems with two zones separated by a straight line having a unique finite singular point which is a node or a focus. The sufficient and necessary conditions for existence and uniqueness of limit cycles are also given.
       
  • On the existence of oscillating solutions in non-monotone Mean-Field Games
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Marco CirantAbstractFor non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial solutions. These non-trivial solutions are in particular shown to exhibit an oscillatory behaviour when they are close to the trivial (constant) one. The existence of such branches is derived using local and global bifurcation methods, that rely on the analysis of eigenfunction expansions of solutions to the associated linearized problem. Numerical analysis is performed on two different models to observe the oscillatory behaviour of solutions predicted by bifurcation theory, and to study further properties of branches far away from bifurcation points.
       
  • Global classical solvability and generic infinite-time blow-up in
           quasilinear Keller–Segel systems with bounded sensitivities
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Michael WinklerAbstractThe chemotaxis system(⋆){ut=∇⋅(D(u,v)∇u)−∇⋅(S(u,v)∇v),vt=Δv−v+u, is considered under homogeneous Neumann boundary conditions in a bounded domain Ω⊂Rn, n≥2, along with initial conditions involving suitably regular and nonnegative data.It is firstly asserted that if the positive smooth function D decays at most algebraically with respect to u, then for any smooth nonnegative and bounded S fulfilling a further mild assumption especially satisfied when S≡S(u) with S(0)=0, (⋆) possesses a globally defined classical solution.If Ω is a ball, then under appropriate assumptions on D and S generalizing the prototypical choices in(⋆⋆)D(u,v)=(u+1)m−1andS(u,v)=u(u+1)σ−1,u≥0,v≥0, with m∈R and σ∈R such that(⋆⋆⋆)m−n−2n
       
  • The L p dual Minkowski problem for p > 1 and q > 0
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Károly J. Böröczky, Ferenc FodorAbstractGeneral Lp dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. Lp dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the Lp dual Minkowski problem, which concerns the characterization of Lp dual curvature measures. In this paper, we solve the existence part of the Lp dual Minkowski problem for p>1 and q>0, and we also discuss the regularity of the solution.
       
  • Local boundedness of solutions to non-local parabolic equations modeled on
           the fractional p-Laplacian
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Martin StrömqvistAbstractWe state and prove estimates for the local boundedness of subsolutions of non-local, possibly degenerate, parabolic integro-differential equations of the form∂tu(x,t)+P.V.∫RnK(x,y,t) u(x,t)−u(y,t) p−2(u(x,t)−u(y,t))dy=0, (x,t)∈Rn×R, where P.V. means in the principle value sense, p∈(1,∞) and the kernel obeys K(x,y,t)≈ x−y n+ps for some s∈(0,1), uniformly in (x,y,t)∈Rn×Rn×R.
       
  • Two-locus clines maintained by diffusion and recombination in a
           heterogeneous environment
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Linlin Su, King-Yeung Lam, Reinhard BürgerAbstractWe study existence and stability of stationary solutions of a system of semilinear parabolic partial differential equations that occurs in population genetics. It describes the evolution of gamete frequencies in a geographically structured population of migrating individuals in a bounded habitat. Fitness of individuals is determined additively by two recombining, diallelic genetic loci that are subject to spatially varying selection. Migration is modeled by diffusion. Of most interest are spatially non-constant stationary solutions, so-called clines. In a two-locus cline all four gametes are present in the population, i.e., it is an internal stationary solution. We provide conditions for existence and linear stability of a two-locus cline if recombination is either sufficiently weak or sufficiently strong relative to selection and diffusion. For strong recombination, we also prove uniqueness and global asymptotic stability. For arbitrary recombination, we determine the stability properties of the monomorphic equilibria, which represent fixation of a single gamete.
       
  • L 1-convergence rates to the Barenblatt solution for the damped
           compressible Euler equations
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Shifeng Geng, Feimin HuangAbstractIn our previous work [17], it is shown that any L∞ weak entropy solution of damped compressible Euler equation converges to the Barrenblatt's solution with finite mass in L1 norm with a convergence rate for 1
       
  • Well-posedness of the free boundary problem for incompressible
           elastodynamics
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Xianpeng Hu, Yongting HuangAbstractThe free boundary problem for the three dimensional incompressible elastodynamics system is studied under the Rayleigh–Taylor sign condition. Both the columns of the elastic stress FF⊤−I and the transpose of the deformation gradient F⊤−I are tangential to the boundary which moves with the velocity, and the pressure vanishes outside the flow domain. The linearized equation takes the form of wave equation in terms of the flow map in the Lagrangian coordinate, and the local-in-time existence of a unique smooth solution is proved using a geometric argument in the spirit of [19].
       
  • Controllability results for the Moore–Gibson–Thompson equation arising
           in nonlinear acoustics
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Carlos Lizama, Sebastián ZamoranoAbstractWe show that the Moore–Gibson–Thomson equationτ∂ttty+α∂tty−c2Δy−bΔ∂ty=k∂tt(y2)+χω(t)u, is controlled by a force that is supported on an moving subset ω(t) of the domain, satisfying a geometrical condition. Using the concept of approximately outer invertible map, a generalized implicit function theorem and assuming that γ:=α−τc2b>0, the local null controllability in the nonlinear case is established. Moreover, the analysis of the critical value γ=0 for the linear equation is included.
       
  • Translating solitons in Riemannian products
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Jorge H.S. de Lira, Francisco MartínAbstractIn this paper we study solitons invariant with respect to the flow generated by a complete parallel vector field in a ambient Riemannian manifold. A special case occurs when the ambient manifold is the Riemannian product (R×P,dt2+g0) and the parallel field is X=∂t. Similarly to what happens in the Euclidean setting, we call them translating solitons. We see that a translating soliton in R×P can be seen as a minimal submanifold for a weighted volume functional. Moreover we show that this kind of solitons appear in a natural way in the context of a monotonicity formula for the mean curvature flow in R×P. When g0 is rotationally invariant and its sectional curvature is non-positive, we are able to characterize all the rotationally invariant translating solitons. Furthermore, we use these families of new examples as barriers to deduce several non-existence results.
       
  • Stability of peakons for the generalized modified Camassa–Holm
           equation
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Zihua Guo, Xiaochuan Liu, Xingxing Liu, Changzheng QuAbstractIn this paper, we study orbital stability of peakons for the generalized modified Camassa–Holm (gmCH) equation, which is a natural higher-order generalization of the modified Camassa–Holm (mCH) equation, and admits Hamiltonian form and single peakons. We first show that the single peakon is the usual weak solution of the PDEs. Some sign invariant properties and conserved densities are presented. Next, by constructing the corresponding auxiliary function h(t,x) and establishing a delicate polynomial inequality relating to the two conserved densities with the maximal value of approximate solutions, the orbital stability of single peakon of the gmCH equation is verified. We introduce a new approach to prove the key inequality, which is different from that used for the mCH equation. This extends the result on the stability of peakons for the mCH equation (Qu et al. 2013) [36] successfully to the higher-order case, and is helpful to understand how higher-order nonlinearities affect the dispersion dynamics.
       
  • Pulsating fronts and front-like entire solutions for a
           reaction–advection–diffusion competition model in a periodic habitat
    • Abstract: Publication date: 5 June 2019Source: Journal of Differential Equations, Volume 266, Issue 12Author(s): Li-Jun Du, Wan-Tong Li, Shi-Liang WuAbstractThis paper is devoted to the study of pulsating fronts and pulsating front-like entire solutions for a reaction–advection–diffusion model of two competing species in a periodic habitat. Under certain assumptions, the competition system admits a leftward and a rightward pulsating fronts in the bistable case. In this work we construct some other types of entire solutions by interacting the leftward and rightward pulsating fronts. Some of these entire solutions behave as the two pulsating fronts approaching each other from both sides of the x-axis, which turn out to be unique and Liapunov stable 2-dimensional manifolds of solutions, furthermore, the leftward and rightward pulsating fronts are on the boundary of these 2-dimensional manifolds. The others behave as the two pulsating fronts propagating from one side of the x-axis, the faster one then invades the slower one as t→+∞. These kinds of pulsating front-like entire solutions then provide some new spreading ways other than pulsating fronts for two strongly competing species interacting in a heterogeneous habitat.
       
  • Robustly topological mixing of Kan's map
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Shaobo Gan, Yi ShiAbstractIn 1994, I. Kan constructed a smooth map on the annulus admitting two physical measures, whose basins are intermingled. In this paper, we prove that Kan's map is C2 robustly topologically mixing.
       
  • Cauchy problem for the ellipsoidal BGK model for polyatomic particles
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Sa Jun Park, Seok-Bae YunAbstractWe establish the existence and uniqueness of mild solutions for the polyatomic ellipsoidal BGK model, which is a relaxation type kinetic model describing the evolution of polyatomic gaseous system at the mesoscopic level.
       
  • Proof of Artés–Llibre–Valls's conjectures for the Higgins–Selkov
           and the Selkov systems
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Hebai Chen, Yilei TangAbstractThe aim of this paper is to prove Artés–Llibre–Valls's conjectures on the uniqueness of limit cycles for the Higgins–Selkov system and the Selkov system. In order to apply the limit cycle theory for Liénard systems, we change the Higgins–Selkov and the Selkov systems into Liénard systems first. Then, we present two theorems on the nonexistence of limit cycles of Liénard systems. At last, the conjectures can be proven by these theorems and some techniques applied for Liénard systems.
       
  • Random attractor for the 3D viscous primitive equations driven by
           fractional noises
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Guoli ZhouAbstractWe develop a new and general method to prove the existence of the random attractor (strong attractor) for the primitive equations (PEs) of large-scale ocean and atmosphere dynamics under non-periodic boundary conditions and driven by infinite-dimensional additive fractional Wiener processes. In contrast to our new method, the common method, compact Sobolev embedding theorem, is to obtain the time-uniform a priori estimates in some Sobolev space whose regularity is higher than the solution space. But this method can not be applied to the 3D stochastic PEs with the non-periodic boundary conditions. Therefore, the existence of universal attractor (weak attractor) was established in previous works (see [15], [16]). The main idea of our method is that we first derive that P-almost surely the solution operator of stochastic PEs is compact. Then we construct a compact absorbing set by virtue of the compact property of the solution operator and the existence of a absorbing set. We should point out that our method has some advantages over the common method of using compact Sobolev embedding theorem, i.e., using our method we only need to obtain time-uniform a priori estimates in the solution space to prove the existence of random attractor for the corresponding stochastic system, while the common method need to establish time-uniform a priori estimates in a more regular functional space than the solution space. Take the stochastic PEs for example, as the unique strong solution to the stochastic PEs belongs to C([0,T];(H1(℧))3), in view of our method, we only need to obtain the time-uniform a priori estimates in the solution space (H1(℧))3 to prove the existence of random attractor for this stochastic system, while the common method need to establish time-uniform a priori estimates for the solution in the functional space (H2(℧))3. However, time-uniform a priori estimates in (H2(℧))3 for the solution to stochastic PEs are too difficult to be established. The present work provides a general way for proving the existence of random attractor for common classes of dissipative stochastic partial differential equations driven by Wiener noises, fractional noises and even jump noises. In a forth coming paper, using this new method we [46] prove the existence of random attractor for the stochastic nematic liquid crystals equations. This is the first result about the long-time behavior of stochastic nematic liquid crystals equations.
       
  • Decay of solutions for 2D Navier–Stokes equations posed on Lipschitz and
           smooth bounded and unbounded domains
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): N.A. Larkin, M.V. PadilhaAbstractInitial–boundary value problems for 2D Navier–Stokes equations posed on bounded and unbounded rectangles as well as on bounded and unbounded smooth domains were considered. The existence and uniqueness of regular global solutions in bounded rectangles and bounded smooth domains as well as exponential decay of solutions on bounded and unbounded domains were established.
       
  • Existence for evolutionary problems with linear growth by stability
           methods
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Verena Bögelein, Frank Duzaar, Leah Schätzler, Christoph SchevenAbstractWe establish that solutions to the Cauchy–Dirichlet problem∂tu−div(Dξf(x,Du))=0 for functionals f:Ω×RN×n→[0,∞) of linear growth can be obtained as limits of solutions to flows with p-growth in the limit p↓1. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.
       
  • Singular Sturmian separation theorems on unbounded intervals for linear
           Hamiltonian systems
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Peter Šepitka, Roman Šimon HilscherAbstractIn this paper we develop new fundamental results in the Sturmian theory for nonoscillatory linear Hamiltonian systems on an unbounded interval. We introduce a new concept of a multiplicity of a focal point at infinity for conjoined bases and, based on this notion, we prove singular Sturmian separation theorems on an unbounded interval. The main results are formulated in terms of the (minimal) principal solutions at both endpoints of the considered interval, and include exact formulas as well as optimal estimates for the numbers of proper focal points of one or two conjoined bases. As a natural tool we use the comparative index, which was recently implemented into the theory of linear Hamiltonian systems by the authors and independently by J. Elyseeva. Throughout the paper we do not assume any controllability condition on the system. Our results turn out to be new even in the completely controllable case.
       
  • Completely degenerate lower-dimensional invariant tori for Hamiltonian
           system
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Shengqing Hu, Bin LiuAbstractWe study the persistence of lower-dimensional invariant tori for a nearly integrable completely degenerate Hamiltonian system. It is shown that the majority of unperturbed invariant tori can survive from the perturbations which are only assumed the smallness and smoothness.
       
  • Compactness of sign-changing solutions to scalar curvature-type equations
           with bounded negative part
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Bruno Premoselli, Jérôme VétoisAbstractWe consider the equation Δgu+hu= u 2⁎−2u in a closed Riemannian manifold (M,g), where h∈C0,θ(M), θ∈(0,1) and 2⁎=2nn−2, n:=dim⁡(M)≥3. We obtain a sharp compactness result on the sets of sign-changing solutions whose negative part is a priori bounded. We obtain this result under the conditions that n≥7 and h
       
  • Blow-up phenomena for the Liouville equation with a singular source of
           integer multiplicity
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Teresa D'AprileAbstractWe are concerned with the existence of blowing-up solutions to the following boundary value problem−Δu=λa(x)eu−4πNδ0 in Ω,u=0 on ∂Ω, where Ω is a smooth and bounded domain in R2 such that 0∈Ω, a(x) is a positive smooth function, N is a positive integer and λ>0 is a small parameter. Here δ0 defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution uλ blowing up at 0 and satisfying λ∫Ωa(x)euλ→8π(N+1) as λ→0+.
       
  • Minimal-speed selection of traveling waves to the Lotka–Volterra
           competition model
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Ahmad Alhasanat, Chunhua OuAbstractIn this paper the minimal-speed determinacy of traveling wave fronts of a two-species competition model of diffusive Lotka–Volterra type is investigated. First, a cooperative system is obtained from the classical Lotka–Volterra competition model. Then, we apply the upper-lower solution technique on the cooperative system to study the traveling waves as well as its minimal-speed selection mechanisms: linear or nonlinear. New types of upper and lower solutions are established. Previous results for the linear speed selection are extended, and novel results on both linear and nonlinear selections are derived.
       
  • The role of protection zone on species spreading governed by a
           reaction–diffusion model with strong Allee effect
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Kai Du, Rui Peng, Ningkui SunAbstractIt is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity. Such a phenomenon, which is termed as the strong Allee effect, is well supported by numerous evidence from ecosystems, mainly due to the environmental pollution as well as unregulated harvesting and hunting. To save an endangered species, in this paper we introduce a protection zone that is governed by a Fisher–KPP nonlinearity, and examine the dynamics of a reaction–diffusion model with strong Allee effect and protection zone. We show the existence of two critical values 0
       
  • Asymptotic stability of superposition of stationary solutions and
           rarefaction waves for 1D Navier–Stokes/Allen–Cahn system
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Haiyan Yin, Changjiang ZhuAbstractIn this paper, we investigate the large time behavior of the solutions to the inflow problem for the one-dimensional Navier–Stokes/Allen–Cahn system in the half space. First, we assume that the space-asymptotic states (ρ+,u+,χ+) and the boundary data (ρb,ub,χb) satisfy some conditions so that the time-asymptotic state of solutions for the inflow problem is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. Then, we show the existence of the stationary solution by the center manifold theorem. Finally, we prove that the nonlinear wave is asymptotically stable when the initial data is a small perturbation of the nonlinear wave. The proof is mainly based on the energy method by taking into account the effect of the concentration χ and the complexity of nonlinear wave.
       
  • Positive solutions for a class of singular quasilinear Schrödinger
           equations with critical Sobolev exponent
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Zhouxin LiAbstractWe prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth−Δu−λc(x)u−κα(Δ( u 2α)) u 2α−2u= u q−2u+ u 2⁎−2u,u∈D1,2(RN), via variational methods, where λ≥0, c:RN→R+, κ>0, 0
       
  • Uniform stability of semilinear wave equations with arbitrary local memory
           effects versus frictional dampings
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Kun-Peng Jin, Jin Liang, Ti-Jun XiaoAbstractThis paper is concerned with the mixed initial–boundary value problem for semilinear wave equations with complementary frictional dampings and memory effects. We successfully establish uniform exponential and polynomial decay rates for the solutions to this initial–boundary value problem under much weak conditions concerning memory effects. More specifically, we obtain the exponential and polynomial decay rates after removing the fundamental condition that the memory-effect region includes a part of the system boundary, while the condition is a necessity in the previous literature; moreover, for the polynomial decay rates we only assume minimal conditions on the memory kernel function g, without the usual assumption of g′ controlled by g.
       
  • Asymptotic regularity of trajectory attractor and trajectory statistical
           solution for the 3D globally modified Navier–Stokes equations
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Caidi Zhao, Tomás CaraballoAbstractWe first prove the existence and regularity of the trajectory attractor for a three-dimensional system of globally modified Navier–Stokes equations. Then we use the natural translation semigroup and trajectory attractor to construct the trajectory statistical solutions in the trajectory space. In our construction the trajectory statistical solution is an invariant Borel probability measure, which is supported by the trajectory attractor and is invariant under the action of the translation semigroup. As a byproduct of the regularity of the trajectory attractor, we obtain the asymptotic regularity of the trajectory statistical solution in the sense that it is supported by a set in the trajectory space in which all weak solutions are in fact strong solutions.
       
  • Self-similar solutions for dyadic models of the Euler equations
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): In-Jee JeongAbstractWe show existence of self-similar solutions satisfying Kolmogorov's scaling for generalized dyadic models of the Euler equations, extending a result of Barbato, Flandoli, and Morandin [1]. The proof is based on the analysis of certain dynamical systems on the plane.
       
  • Long time behavior of solutions to the 3D Hall-magneto-hydrodynamics
           system with one diffusion
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Mimi Dai, Han LiuAbstractThis paper studies the asymptotic behavior of smooth solutions to the generalized Hall-magneto-hydrodynamics system (1.1) with one single diffusion on the whole space R3. We establish that, in the inviscid resistive case, the energy ‖b(t)‖22 vanishes and ‖u(t)‖22 converges to a constant as time tends to infinity provided the velocity is bounded in W1−α,3α(R3); in the viscous non-resistive case, the energy ‖u(t)‖22 vanishes and ‖b(t)‖22 converges to a constant provided the magnetic field is bounded in W1−β,∞(R3). In summary, one single diffusion, being as weak as (−Δ)αb or (−Δ)βu with small enough α,β, is sufficient to prevent asymptotic energy oscillations for certain smooth solutions to the system.
       
  • Asymptotics for periodic systems
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Lassi Paunonen, David SeifertAbstractThis paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class of dissipative systems arising naturally in applications. For this class of systems we analyse in detail the spectral properties of the associated monodromy operator, showing in particular that it is a so-called Ritt operator under a natural ‘resonance’ condition. This allows us to deduce from our general result a precise description of the asymptotic behaviour of the corresponding solutions. In particular, we present conditions for rational rates of convergence to periodic solutions in the case where the convergence fails to be uniformly exponential. We illustrate our general results by applying them to concrete problems including the one-dimensional wave equation with periodic damping.
       
  • The transport equation in the scaling invariant Besov or
           Essén–Janson–Peng–Xiao space
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Jie XiaoAbstractThis paper addresses a well-posedness of the weak solution to the transport equation (describing how a scalar quantity is transported in a space) with an initial data in the scaling invariant Besov or Essén–Janson–Peng–Xiao space via the boundedness of the left and right compositions acting on each space.
       
  • On the concentration phenomenon of L 2-subcritical constrained minimizers
           for a class of Kirchhoff equations with potentials
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Gongbao Li, Hongyu YeAbstractIn this paper, we study the existence and concentration behavior of minimizers for iV(c)=infu∈Sc⁡IV(u), here Sc={u∈H1(RN) ∫RNV(x) u 20} andIV(u)=12∫RN(a ∇u 2+V(x) u 2)+b4(∫RN ∇u 2)2−1p∫RN u p, where N=1,2,3 and a,b>0 are constants. By the Gagliardo–Nirenberg inequality, we get the sharp existence of global constraint minimizers of iV(c) for 2
       
  • Geometric stability switch criteria in delay differential equations with
           two delays and delay dependent parameters
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Qi An, Edoardo Beretta, Yang Kuang, Chuncheng Wang, Hao WangAbstractMost modeling efforts involve multiple physical or biological processes. All physical or biological processes take time to complete. Therefore, multiple time delays occur naturally and shall be considered in more advanced modeling efforts. Carefully formulated models of such natural processes often involve multiple delays and delay dependent parameters. However, a general and practical theory for the stability analysis of models with more than one discrete delay and delay dependent parameters is nonexistent. The main purpose of this paper is to present a practical geometric method to study the stability switching properties of a general transcendental equation which may result from a stability analysis of a model with two discrete time delays and delay dependent parameters that dependent only on one of the time delay. In addition to simple and illustrative examples, we present a detailed application of our method to the study of a two discrete delay SIR model.
       
  • Non-coercive Lyapunov functions for infinite-dimensional systems
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Andrii Mironchenko, Fabian WirthAbstractWe show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied. For evolution equations in Banach spaces with Lipschitz continuous nonlinearities these additional assumptions become especially simple. The results encompass some recent results on linear switched systems on Banach spaces. Finally, we derive new non-coercive converse Lyapunov theorems and give some examples showing the necessity of our assumptions.
       
  • Nonlocal scalar field equations: Qualitative properties, asymptotic
           profiles and local uniqueness of solutions
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Mousomi Bhakta, Debangana MukherjeeAbstractWe study the nonlocal scalar field equation with a vanishing parameter:(Pϵ){(−Δ)su+ϵu= u p−2u− u q−2uinRNu∈Hs(RN), where s∈(0,1), N>2s, q>p>2 are fixed parameters and ϵ>0 is a vanishing parameter. For ϵ small, we prove the existence and qualitative properties of positive solutions. Next, we study the asymptotic behavior of ground state solutions when p is subcritical, supercritical or critical Sobolev exponent 2⁎=2NN−2s. For p2⁎, the solution asymptotically coincides with a ground-state solution of (−Δ)su=up−uq. Furthermore, using these asymptotic profile of positive solutions, we establish the local uniqueness of positive solution.
       
  • The 1:1 resonance in Hamiltonian systems
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Heinz Hanßmann, Igor HoveijnAbstractTwo-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as parameters, the system undergoes a bifurcation when the frequencies pass through a resonance. These bifurcations are well understood for most resonances k:l, but not the semisimple cases 1:1 and 1:−1. A two-degree-of-freedom Hamiltonian system can be approximated to any order by an integrable normal form. The reason is that the normal form of a Hamiltonian system has an additional integral due to the normal form symmetry. The latter is intimately related to the ratio of the frequencies. For a rational frequency ratio this leads to S1-symmetric systems. The question we wish to address is about the co-dimension of such a system in 1:1 resonance with respect to left-right-equivalence, where the right action is S1-equivariant. The result is a co-dimension five unfolding of the central singularity. Two of the unfolding parameters are moduli and the remaining non-modal parameters are the ones found in the linear unfolding of this system.
       
  • Lagrange stability for impulsive Duffing equations
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Jianhua Shen, Lu Chen, Xiaoping YuanAbstractThis work discusses the boundedness of solutions for impulsive Duffing equation with time-dependent polynomial potentials. By KAM theorem, we prove that all solutions of the Duffing equation with low regularity in time undergoing suitable impulses are bounded for all time and that there are many (positive Lebesgue measure) quasi-periodic solutions clustering at infinity. This result extends some well-known results on Duffing equations to impulsive Duffing equations.
       
  • Spectral theory approach for a class of radial indefinite variational
           problems
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Liliane A. Maia, Mayra SoaresAbstractConsidering the radial nonlinear Schrödinger equation(Pr)−Δu+V(x)u=g(x,u) inRN,N≥3 we aim to find a radial nontrivial solution for it, where V changes sign ensuring problem (Pr) is indefinite and g is an asymptotically linear nonlinearity. We work with variational methods associating problem (Pr) to an indefinite functional in order to apply our Abstract Linking Theorem for Cerami sequences in [8] to get a non-trivial critical point for this functional. Our goal is to make use of spectral properties of operator A:=Δ+V(x) restricted to Hrad1(RN), the space of radially symmetric functions in H1(RN), for obtaining a linking geometry structure to the problem and by means of special properties of radially symmetric functions get the necessary compactness.
       
  • Uniqueness for an inverse problem for a nonlinear parabolic system with an
           integral term by one-point Dirichlet data
    • Abstract: Publication date: 15 May 2019Source: Journal of Differential Equations, Volume 266, Issue 11Author(s): Dietmar Hömberg, Shuai Lu, Masahiro YamamotoAbstractWe consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic inverse heat source problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement.
       
  • Solvability for a drift-diffusion system with Robin boundary conditions
    • Abstract: Publication date: Available online 21 March 2019Source: Journal of Differential EquationsAuthor(s): A. Heibig, A. Petrov, C. ReichertAbstractThis paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally, two examples coming from the corrosion and the self-gravitation model are analyzed.
       
  • On the fourth order Schrödinger equation in four dimensions: Dispersive
           estimates and zero energy resonances
    • Abstract: Publication date: Available online 21 March 2019Source: Journal of Differential EquationsAuthor(s): William R. Green, Ebru ToprakAbstractWe study the fourth order Schrödinger operator H=(−Δ)2+V for a decaying potential V in four dimensions. In particular, we show that the t−1 decay rate holds in the L1→L∞ setting if zero energy is regular. Furthermore, if the threshold energies are regular then a faster decay rate of t−1(log⁡t)−2 is attained for large t, at the cost of logarithmic spatial weights. Zero is not regular for the free equation, hence the free evolution does not satisfy this bound due to the presence of a resonance at the zero energy. We provide a full classification of the different types of zero energy resonances and study the effect of each type on the time decay in the dispersive bounds.
       
  • Hill-type formula for Hamiltonian system with Lagrangian boundary
           conditions
    • Abstract: Publication date: Available online 21 March 2019Source: Journal of Differential EquationsAuthor(s): Xijun Hu, Yuwei Ou, Penghui WangAbstractIn this paper, we build up Hill-type formula for linear Hamiltonian systems with Lagrangian boundary conditions, which include standard Neumann, Dirichlet boundary conditions. Such a kind of boundary conditions comes from the N-reversible symmetry periodic orbits in n-body problem naturally, where N is an anti-symplectic orthogonal matrix with N2=I. The Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary conditions. Consequently, we derive the Krein-type trace formula and give nontrivial estimation for the eigenvalue problem. Combined with the Maslov-type index theory, we give some new stability criteria for the N-reversible symmetry periodic solutions of Hamiltonian systems. As an application, we study the linear stability of elliptic relative equilibria in planar 3-body problem.
       
  • Dynamic and asymptotic behavior of singularities of certain weak KAM
           solutions on the torus
    • Abstract: Publication date: Available online 21 March 2019Source: Journal of Differential EquationsAuthor(s): Piermarco Cannarsa, Qinbo Chen, Wei ChengAbstractFor mechanical Hamiltonian systems on the torus, we study the dynamical properties of the generalized characteristic semiflows associated with the Hamilton-Jacobi equations, and build the relation between the ω-limit sets of the semiflows and the projected Aubry sets.
       
  • Mean Li-Yorke chaos for random dynamical systems
    • Abstract: Publication date: Available online 21 March 2019Source: Journal of Differential EquationsAuthor(s): Yunping Wang, Ercai Chen, Xiaoyao ZhouAbstractIn this paper, we studied the complexity of some random dynamical systems with positive topological entropy. The random dynamical systems are usually generated by stochastic partial differential equations (SPDEs) and contain randomness in many ways. We proved that there exists mean Li-Yorke chaotic phenomenon in some random dynamical systems with positive entropy.
       
  • Nonlinear multiparameter eigenvalue problems: Linearised and nonlinearised
           solutions
    • Abstract: Publication date: Available online 20 March 2019Source: Journal of Differential EquationsAuthor(s): V.Yu. Kurseeva, S.V. Tikhov, D.V. ValovikAbstractThe paper focuses on a nonlinear multiparameter eigenvalue problem called P. This problem involves n spectral parameters and also depends on n2 numerical parameters, where n⩾2 is an integer. If these numerical parameters vanish, P degenerates into n linear (one-parameter) eigenvalue problems called Pi0 (i=1,n‾). In connection with P one can consider another n nonlinear one-parameter eigenvalue problems called Pi. The problems Pi have eigenvalues with as well as without linear counterparts. The paper suggests to consider Pi as ‘nonunperturbed’ instead of Pi0. Using properties of eigenvalues of Pi, one manages to prove existence of eigentuples of P. Among the eigentuples found in this way, there are eigetuples with as well as without linear counterparts. Results of the paper are found with a nonclassical approach. Applications of the found results to nonlinear optics are shown.
       
  • Homogenization of an advection equation with locally stationary random
           coefficients
    • Abstract: Publication date: Available online 18 March 2019Source: Journal of Differential EquationsAuthor(s): Tymoteusz Chojecki, Tomasz KomorowskiAbstractIn the paper we consider the solution of an advection equation with rapidly changing coefficients ∂tuε+(1/ε)V(t/ε2,x/ε)⋅∇xuε=0 for t0 is some small parameter and the drift term (V(t,x))(t,x)∈R1+d is assumed to be a d-dimensional, vector valued random field with incompressible spatial realizations. We prove that when the field is Gaussian, locally stationary, quasi-periodic in the x variable and strongly mixing in time the solutions uε(t,x) converge in law, as ε→0, to u0(x(T;t,x)), where (x(s;t,x))s≥t is a diffusion satisfying x(t;t,x)=x. The averages of uε(T,x) converge then to the solution of the corresponding Kolmogorov backward equation.
       
  • On the simplicity of eigenvalues of two nonhomogeneous Euler-Bernoulli
           beams connected by a point mass
    • Abstract: Publication date: Available online 18 March 2019Source: Journal of Differential EquationsAuthor(s): Jamel Ben Amara, Hedi BouzidiAbstractIn this paper we consider a linear system modeling the vibrations of two nonhomogeneous Euler-Bernoulli beams connected by a point mass. This system is generated by the following equationsρ(x)ytt(t,x)+(σ(x)yxx(t,x))xx−(q(x)yx(t,x))x=0,t>0,x∈(−1,0)∪(0,1),Mytt(t,0)=(Ty(t,x)) x=0−−(Ty(t,x)) x=0+,t>0, with hinged boundary conditions at both ends, where M>0, ρ(x)>0,σ(x)>0, q(x)≥0 and Ty=(σ(x)yxx)x−q(x)yx for x∈(−1,0)∪(0,1). We prove that all the associated eigenvalues (λn)n≥1 are algebraically simple, furthermore the corresponding eigenfunctions (ϕn)n≥1 satisfy ϕn′(−1
       
  • Measure N-expansive systems
    • Abstract: Publication date: Available online 18 March 2019Source: Journal of Differential EquationsAuthor(s): K. Lee, C.A. Morales, B. San MartinAbstractThe N-expansive systems have been recently studied in the literature [6], [7], [9], [14]. Here we characterize them as those homeomorphisms for which every Borel probability measure is N-expansive. In particular, the strongly measure expansive homeomorphisms in the sense of [8] are precisely the homeomorphisms for which every invariant measure is 1-expansive. We also characterize the 1-expansive measures for equicontinuous homeomorphisms as the convex sum of finitely many Dirac measures supported on isolated points. In particular, such measures do not exist on metric spaces without isolated points. Furthermore, we consider N-expansive measure for flows and prove that a flow is N-expansive in the sense of [9] if and only if every Borel probability measure is N-expansive. Finally, we obtain a lower bound of the topological entropy of the N-expansive flows as the exponential growth rate of the number of periodic orbits.
       
  • Unique recovery of lower order coefficients for hyperbolic equations from
           data on disjoint sets
    • Abstract: Publication date: Available online 15 March 2019Source: Journal of Differential EquationsAuthor(s): Yavar Kian, Yaroslav Kurylev, Matti Lassas, Lauri OksanenAbstractWe consider a restricted Dirichlet-to-Neumann map ΛS,RT associated with the operator ∂t2−Δg+A+q where Δg is the Laplace-Beltrami operator of a Riemannian manifold (M,g), and A and q are a vector field and a function on M. The restriction ΛS,RT corresponds to the case where the Dirichlet traces are supported on (0,T)×S and the Neumann traces are restricted on (0,T)×R. Here S and R are open sets, which may be disjoint, on the boundary of M. We show that ΛS,RT determines uniquely, up the natural gauge invariance, the lower order terms A and q in a neighborhood of the set R assuming that R is strictly convex and that the wave equation is exactly controllable from S in time T/2. We give also a global result under a convex foliation condition. The main novelty is the recovery of A and q when the sets R and S are disjoint. We allow A and q to be non-self-adjoint, and in particular, the corresponding physical system may have dissipation of energy.
       
  • Stability of strong solutions for a model of incompressible two–phase
           flow under thermal fluctuations
    • Abstract: Publication date: Available online 15 March 2019Source: Journal of Differential EquationsAuthor(s): Eduard Feireisl, Madalina PetcuAbstractWe consider a model of a two–phase flow based on the phase field approach, where the fluid bulk velocity obeys the standard Navier–Stokes system while the concentration difference of the two fluids plays a role of order parameter governed by the Allen–Cahn equations. Possible thermal fluctuations are incorporated through a random forcing term in the Allen–Cahn equation. We show that suitable dissipative martingale solutions satisfy a stochastic version of the relative energy inequality. This fact is used for showing the weak–strong uniqueness principle both pathwise and in law.
       
  • Recovery of an embedded obstacle and the surrounding medium for Maxwell's
           system
    • Abstract: Publication date: Available online 15 March 2019Source: Journal of Differential EquationsAuthor(s): Youjun Deng, Hongyu Liu, Xiaodong LiuAbstractIn this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques.
       
  • The Γ-limit of traveling waves in the FitzHugh-Nagumo system
    • Abstract: Publication date: Available online 15 March 2019Source: Journal of Differential EquationsAuthor(s): Chao-Nien Chen, Yung Sze Choi, Nicola FuscoAbstractPatterns and waves are basic and important phenomena that govern the dynamics of physical and biological systems. A common theme in investigating such systems is to identify the intrinsic factors responsible for such self-organization. The Γ-convergence is a well-known technique applicable to variational formulations of concentration phenomena of stable patterns. Recently a geometric variational functional associated with the Γ-limit of standing waves of the FitzHugh-Nagumo system has been built. This article studies the Γ-limit of traveling waves. To the best of our knowledge, this is the first attempt to expand the scope of applicability of Γ-convergence to cover non-stationary problems.
       
  • The point-interaction approximation for the fields generated by contrasted
           bubbles at arbitrary fixed frequencies
    • Abstract: Publication date: Available online 15 March 2019Source: Journal of Differential EquationsAuthor(s): Habib Ammari, Durga Prasad Challa, Anupam Pal Choudhury, Mourad SiniAbstractWe deal with the linearized model of the acoustic wave propagation generated by small bubbles in the harmonic regime. We estimate the waves generated by a cluster of M small bubbles, distributed in a bounded domain Ω, with relative densities having contrasts of the order aβ,β>0, where a models their relative maximum diameter, a≪1. We provide useful and natural conditions on the number M, the minimum distance and the contrasts parameter β of the small bubbles under which the point interaction approximation (called also the Foldy-Lax approximation) is valid.With the regimes allowed by our conditions, we can deal with a general class of such materials. Applications of these expansions in material sciences and imaging are immediate. For instance, they are enough to derive and justify the effective media of the cluster of the bubbles for a class of gases with densities having contrasts of the order aβ, β∈(32,2) and in this case we can handle any fixed frequency. In the particular and important case β=2, we can handle any fixed frequency far or close (but distinct) from the corresponding Minnaert resonance. The cluster of the bubbles can be distributed to generate volumetric metamaterials but also low dimensional ones as metascreens and metawires.
       
  • Bifurcation analysis of an SIRS epidemic model with a generalized
           nonmonotone and saturated incidence rate
    • Abstract: Publication date: Available online 14 March 2019Source: Journal of Differential EquationsAuthor(s): Min Lu, Jicai Huang, Shigui Ruan, Pei YuAbstractIn this paper, we study a susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone and saturated incidence rate kI2S1+βI+αI2, in which the infection function first increases to a maximum when a new infectious disease emerges, then decreases due to psychological effect, and eventually tends to a saturation level due to crowding effect. It is shown that there are a weak focus of multiplicity at most two and a cusp of codimension at most two for various parameter values, and the model undergoes saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, Hopf bifurcation, and degenerate Hopf bifurcation of codimension two as the parameters vary. It is shown that there exists a critical value α=α0 for the psychological effect, and two critical values k=k0,k1(k0α0, or α≤α0 and k≤k0, the disease will die out for all positive initial populations; (ii) when α=α0 and k0k1, the disease will persist in the form of a positive coexistent steady state for some positive initial populations; and (iv) when αk0, the disease will persist in the form of multiple positive periodic coexistent oscillations and coexistent steady states for some positive initial populations. Numerical simulations, including the existence of one or two limit cycles and data-fitting of the influenza data in Mainland China, are presented to illustrate the theoretical results.
       
  • Dynamics of a nonlocal dispersal SIS epidemic model with Neumann boundary
           conditions
    • Abstract: Publication date: Available online 13 March 2019Source: Journal of Differential EquationsAuthor(s): Fei-Ying Yang, Wan-Tong Li, Shigui RuanAbstractIn this paper we study a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the spatial movement of individuals is described by a nonlocal (convolution) diffusion operator, the transmission rate and recovery rate are spatially heterogeneous, and the total population number is constant. We first define the basic reproduction number R0 and discuss the existence, uniqueness and stability of steady states of the nonlocal dispersal SIS epidemic model in terms of R0. Then we consider the impacts of the large diffusion rates of the susceptible and infectious populations on the persistence and extinction of the disease. The obtained results indicate that the nonlocal movement of the susceptible or infectious individuals will enhance the persistence of the infectious disease. In particular, our analytical results suggest that the spatial heterogeneity tends to boost the spread of the infectious disease.
       
  • Optimal regularity of stochastic evolution equations in M-type 2 Banach
           spaces
    • Abstract: Publication date: Available online 8 March 2019Source: Journal of Differential EquationsAuthor(s): Jialin Hong, Chuying Huang, Zhihui LiuAbstractIn this paper, we prove the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations driven by general multiplicative noises in martingale type 2 Banach spaces. The main idea of our method is to combine the approach in [9] dealing with Hilbert setting and a version of Burkholder inequality in M-type 2 Banach space. Applying our main results to the stochastic heat equation gives a positive answer to an open problem proposed in [10].
       
  • A criterion for the triviality of the centralizer for vector fields and
           applications
    • Abstract: Publication date: Available online 8 March 2019Source: Journal of Differential EquationsAuthor(s): Wescley Bonomo, Paulo VarandasAbstractIn this paper we establish a criterion for the triviality of the C1-centralizer for vector fields and flows. In particular we deduce the triviality of the centralizer at homoclinic classes of Cr vector fields (r≥1). Furthermore, we show that the set of flows whose C1-centralizer is trivial include: (i) C1-generic volume preserving flows, (ii) C2-generic Hamiltonian flows on a generic and full Lebesgue measure set of energy levels, and (iii) C1-open set of non-hyperbolic vector fields (that admit a Lorenz attractor). We also provide a criterion for the triviality of the C0-centralizer of continuous flows.
       
  • R + 3 &rft.title=Journal+of+Differential+Equations&rft.issn=0022-0396&rft.date=&rft.volume=">Time decay rate of global strong solutions to nematic liquid crystal flows
           in R + 3
    • Abstract: Publication date: Available online 6 March 2019Source: Journal of Differential EquationsAuthor(s): Jinrui Huang, Changyou Wang, Huanyao WenAbstractIn this paper, we obtain optimal time-decay rates in Lr(R+3) for r≥1 of global strong solutions to the nematic liquid crystal flows in R+3, provided the initial data has small L3(R+3)-norm.
       
  • Regularity for multi-phase variational problems
    • Abstract: Publication date: Available online 5 March 2019Source: Journal of Differential EquationsAuthor(s): Cristiana De Filippis, Jehan OhAbstractWe prove C1,ν-regularity for local minimizers of the multi-phase energy:w↦∫Ω Dw p+a(x) Dw q+b(x) Dw sdx, under sharp assumptions relating the couples (p,q) and (p,s) to the Hölder exponents of the modulating coefficients a(⋅) and b(⋅), respectively.
       
  • The 2D Boussinesq equations with vertical dissipation and linear stability
           of shear flows
    • Abstract: Publication date: Available online 5 March 2019Source: Journal of Differential EquationsAuthor(s): Lizheng Tao, Jiahong WuAbstractThis paper studies the linear stability of a steady-state solution with the velocity being a shear flow to the 2D Boussinesq equations with only vertical dissipation. The Boussinesq equations model many fluid phenomena when the Boussinesq approximation applies such as the Rayleigh-Benard convection, atmospheric fronts and oceanic circulation. The vertically dissipative 2D Boussinesq equations model geophysical fluids in certain physical regimes. Whether or not the vertical dissipation can damp perturbations near the equilibrium with the velocity being a shear and the temperature being zero is an important but difficult problem. Assuming the spatial domain is periodic in the horizontal direction and half-line in the vertical direction with no flux boundary condition, we show that any perturbation satisfying the linearized equation around this equilibrium is infinitely smooth in the x−variable and decays exponentially in time and in the horizontal Fourier mode, even though the linearized system involves only vertical dissipation.
       
  • Bifurcations of small limit cycles in Liénard systems with cubic
           restoring terms
    • Abstract: Publication date: Available online 5 March 2019Source: Journal of Differential EquationsAuthor(s): Yun Tian, Maoan Han, Fangfang XuAbstractIn this paper, we study bifurcations of small-amplitude limit cycles of Liénard systems of the form x˙=y−F(x), y˙=−g(x), where g(x) is a cubic polynomial, and F(x) is a smooth or piecewise smooth polynomial of degree n. By using involutions, we obtain sharp upper bounds of the number of small-amplitude limit cycles produced around a singular point for some systems of this type.
       
  • Robin eigenvalues on domains with peaks
    • Abstract: Publication date: Available online 5 March 2019Source: Journal of Differential EquationsAuthor(s): Hynek Kovařík, Konstantin PankrashkinAbstractLet Ω⊂RN, N≥2, be a bounded domain with an outward power-like peak which is assumed not too sharp in a suitable sense. We consider the Laplacian u↦−Δu in Ω with the Robin boundary condition ∂nu=αu on ∂Ω with ∂n being the outward normal derivative and α>0 being a parameter. We show that for large α the associated eigenvalues Ej(α) behave as Ej(α)∼−ϵjαν, where ν>2 and ϵj>0 depend on the dimension and the peak geometry. This is in contrast with the well-known estimate Ej(α)=O(α2) for the Lipschitz domains.
       
  • The Cauchy problem for shallow water waves of large amplitude in Besov
           space
    • Abstract: Publication date: Available online 2 March 2019Source: Journal of Differential EquationsAuthor(s): Lili Fan, Wei YanAbstractIn this paper, we consider a nonlinear evolution equation modelling the propagation of surface waves in the shallow water regime of large amplitude, which is characterised by some cubical nonlinearities. First, we establish the local well-posedness in Besov space B2,13/2. Then, we give a blow-up criterion. Finally, with a given analytic initial data, we establish the analyticity of the solutions in both variables, globally in space and locally in time.
       
  • Principle of linearized stability and instability for parabolic partial
           differential equations with state-dependent delay
    • Abstract: Publication date: Available online 2 March 2019Source: Journal of Differential EquationsAuthor(s): Yunfei Lv, Yongzhen Pei, Rong YuanAbstractIn this paper, the stability properties of a parabolic partial differential equation with state-dependent delay are investigated by the heuristic approach. The previous works [1], [2] obtained a continuously differentiable semiflow with continuously differentiable solution operators defined by the classical solutions, and resolved the problem of linearization for this equation. Here, we clarify the relation between the spectral properties of the linearization of the semiflow at a stationary solution and the strong continuous semigroup defined by the solutions of the linearization of this equation, and consider the local stable and unstable invariant manifolds of the semiflow at a stationary solution. By a biological application, we finally verify all hypotheses for an age structured diffusive model with state-dependent delay and consider its stability behavior.
       
  • R N +involving+uΔ(u 2)+and+sign-changing+potentials&rft.title=Journal+of+Differential+Equations&rft.issn=0022-0396&rft.date=&rft.volume=">Solutions for fourth order elliptic equations on R N involving uΔ(u 2)
           and sign-changing potentials
    • Abstract: Publication date: Available online 1 March 2019Source: Journal of Differential EquationsAuthor(s): Shibo Liu, Zhihan ZhaoAbstractWe obtain existence and multiplicity results for fourth order elliptic equations on RN involving uΔ(u2) and sign-changing potentials. Our results generalize some recent results on this kind of problems. To study this kind of problems, we first consider the case that the potential V is coercive so that the working space can be compactly embedded into Lebesgue spaces. Then we studied the case that the potential V is bounded so that the working space is exactly H2(RN), which can not be compactly embedded into Lebesgue spaces anymore. To deal with this more difficult case, we study the weak continuity of the term in the energy functional corresponding to the term uΔ(u2) in the equation.
       
  • Nonlocal dispersal equations in time-periodic media: Principal spectral
           theory, limiting properties and long-time dynamics
    • Abstract: Publication date: Available online 26 February 2019Source: Journal of Differential EquationsAuthor(s): Zhongwei Shen, Hoang-Hung VoAbstractThe present paper is devoted to the investigation of the following nonlocal dispersal equationut(t,x)=Dσm[∫ΩJσ(x−y)u(t,y)dy−u(t,x)]+f(t,x,u(t,x)),t>0,x∈Ω‾, where Ω⊂RN is a bounded and connected domain with smooth boundary, m∈[0,2) is the cost parameter, D>0 is the dispersal rate, σ>0 characterizes the dispersal range, Jσ=1σNJ(⋅σ) is the scaled dispersal kernel, and f is a time-periodic nonlinear function of generalized KPP type. This paper is a continuation of the works of Berestycki et al. [3], [4], where f was assumed to be time-independent. We first study the principal spectral theory of the linear operator associated to the linearization of the equation at u≡0. We establish an easily verifiable, general and sharp sufficient condition for the existence of the principal eigenvalue as well as important sup-inf characterizations of the principal eigenvalue. Next, we study the influences of the principal spectrum point on the global dynamics and confirm that the principal spectrum point being zero is critical. It is followed by the investigation of the effects of the dispersal rate D and the dispersal range characterized by σ on the principal spectrum point and the positive time-periodic solution. In particular, we prove various limiting properties of the principal spectrum point and the positive time-periodic solution as D,σ→0+ or ∞. To achieve these, we develop new techniques to overcome fundamental difficulties caused by the lack of the usual L2 variational formula for the principal eigenvalue, the lack of the regularizing effects of the semigroup generated by the nonlocal dispersal operator, and the presence of the time-dependence of the nonlinearity f. Finally, we establish the maximum principle for time-periodic nonlocal dispersal operators.
       
  • On the influence of gravity on density-dependent incompressible periodic
           fluids
    • Abstract: Publication date: Available online 26 February 2019Source: Journal of Differential EquationsAuthor(s): Van-Sang Ngo, Stefano ScrobognaAbstractThe present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number ε goes to zero. We consider the very general case where the initial data do not have a zero horizontal average, where we only have smoothing effect on the velocity but not on the density and where we can have resonant phenomena on the domain. We explicitly determine the limit system when ε→0 and prove its global wellposedness. Finally, we prove that for large initial data, the density-dependent, incompressible fluid system is globally wellposed, provided that ε is small enough.
       
  • Travelling wave solutions for a non-local evolutionary-epidemic system
    • Abstract: Publication date: Available online 26 February 2019Source: Journal of Differential EquationsAuthor(s): L. Abi Rizk, J.-B. Burie, A. DucrotAbstractIn this work we study the travelling wave solutions for a spatially distributed system of equations modelling the evolutionary epidemiology of plant-pathogen interaction. Here the mutation process is described using a non-local convolution operator in the phenotype space.Using dynamical system ideas coupled with refined estimates on the asymptotic behaviour of the profiles, we prove that the wave solutions have a rather simple structure. This analysis allows us to reduce the infinite dimensional travelling wave profile system of equations to a four dimensional ode system. The latter is used to prove the existence of travelling wave solutions for any wave speed larger than a minimal wave speed c⋆, provided some parameters condition expressed using the principle eigenvalue of some integral operator. It is also used to prove that any travelling wave solution connects two determined stationary states.
       
  • Invariant Cantor manifolds of quasi-periodic solutions for the derivative
           nonlinear Schrödinger equation
    • Abstract: Publication date: Available online 25 February 2019Source: Journal of Differential EquationsAuthor(s): Meina Gao, Jianjun LiuAbstractThis paper is concerned with the derivative nonlinear Schrödinger equation with periodic boundary conditionsiut+uxx+i(f(x,u,u¯))x=0,x∈T:=R/2πZ, where f is an analytic function of the formf(x,u,u¯)=μ u 2u+f≥4(x,u,u¯),0≠μ∈R, and f≥4(x,u,u¯) denotes terms of order at least four in u,u¯. We show the above equation possesses Cantor families of smooth quasi-periodic solutions of small amplitude. The proof is based on an infinite dimensional KAM theorem for unbounded perturbation vector fields.
       
  • Entire solutions to reaction-diffusion equations in multiple half-lines
           with a junction
    • Abstract: Publication date: Available online 25 February 2019Source: Journal of Differential EquationsAuthor(s): Shuichi Jimbo, Yoshihisa MoritaAbstractThere exists a traveling front wave to a bistable reaction-diffusion equation in a whole line under a certain condition of reaction term f(u). We deal with the bistable reaction-diffusion equation with the same f(u) in a domain Ω which is a graph of special type, that is, a union of half-lines starting at a common point, so the domain has a unique junction of the half-lines. The aim of our study is to show the existence of nontrivial entire solutions, which are classical solutions defined for all (x,t)∈Ω×R. We prove that there are entire solutions which converge to the front waves in some of half-lines and converge to zero in the remaining half-lines as t→−∞. We also give a condition under that the entire solutions exhibit the blocking of the front propagation. This blocking is caused by the emergence of stationary solutions. The stability/instability of the stationary solutions are proved.
       
  • Dichotomous solutions for semilinear ill-posed equations with sectorially
           dichotomous operator
    • Abstract: Publication date: Available online 25 February 2019Source: Journal of Differential EquationsAuthor(s): Lianwang Deng, Dongmei XiaoIn this paper, we study a class of semilinear ill-posed equations with sectorially dichotomous operator S on Banach space Z. Firstly we give a direct sum decomposition of Z, Z+⊕Z−=Z, corresponding to spectrum of S such that hyperbolic bisectorial operator S can be split into two sectorial operators S Z+ and −S Z− on Z+ and Z−, respectively. Then we construct the intermediate spaces between whole space Z and domain D(S) of sectorially dichotomous operator S. Following ElBialy's works, we propose the dichotomous initial condition for this semilinear ill-posed equation, and obtain the existence, uniqueness, continuous dependence on the dichotomous initial value, regularity and Zα-estimate of dichotomous solutions. As applications of the results, we give the existence and uniqueness of local solutions for an elliptic PDE in infinite cylindrical domain and an abstract semilinear ill-posed equation with non-dense domain.
       
  • Null-controllability properties of the wave equation with a second order
           memory term
    • Abstract: Publication date: Available online 22 February 2019Source: Journal of Differential EquationsAuthor(s): Umberto Biccari, Sorin MicuAbstractWe study the internal controllability of a wave equation with memory in the principal part, defined on the one-dimensional torus T=R/2πZ. We assume that the control is acting on an open subset ω(t)⊂T, which is moving with a constant velocity c∈R∖{−1,0,1}. The main result of the paper shows that the equation is null controllable in a sufficiently large time T and for initial data belonging to suitable Sobolev spaces. Its proof follows from a careful analysis of the spectrum associated with our problem and from the application of the classical moment method.
       
  • Long time dynamics of Schrödinger and wave equations on flat tori
    • Abstract: Publication date: Available online 21 February 2019Source: Journal of Differential EquationsAuthor(s): M. Berti, A. MasperoWe consider a class of linear time dependent Schrödinger equations and quasi-periodically forced nonlinear Hamiltonian wave/Klein Gordon and Schrödinger equations on arbitrary flat tori. For the linear Schrödinger equation, we prove a tϵ (∀ϵ>0) upper bound for the growth of the Sobolev norms as the time goes to infinity. For the nonlinear Hamiltonian PDEs we construct families of time quasi-periodic solutions.Both results are based on “clusterization properties” of the eigenvalues of the Laplacian on a flat torus and on suitable “separation properties” of the singular sites of Schrödinger and wave operators, which are integers, in space–time Fourier lattice, close to a cone or a paraboloid. Thanks to these properties we are able to apply Delort abstract theorem [20] to control the speed of growth of the Sobolev norms, and Berti–Corsi–Procesi abstract Nash–Moser theorem [8] to construct quasi-periodic solutions.
       
  • Global existence and convergence rates to a chemotaxis-fluids system with
           mixed boundary conditions
    • Abstract: Publication date: Available online 19 February 2019Source: Journal of Differential EquationsAuthor(s): Yingping Peng, Zhaoyin XiangAbstractIn this paper, we investigate the large time behavior of strong solutions to a chemotaxis-fluids system in an unbounded domain with mixed boundary conditions. Based on the anisotropic Lp technique, the elliptic estimates and Stokes estimates, we first establish the global existence of strong solution around the equilibrium state (0,csatn,0) with the help of the continuity arguments, where csatn is the saturation value of oxygen inside the fluid. Then we use De Giorgi's technique and energy method to show that such a solution will converge to (0,csatn,0) with an explicit convergence rate in the chemotaxis-free case. Our assumptions and results are consistent with the experimental descriptions and the numerical analysis. The novelty here consists of deriving some new elliptic estimates and Stokes estimates, and choosing a suitable weight in De Giorgi's technique to deal with the mixed boundary conditions.
       
  • Renormalized solutions to parabolic equations in time and space dependent
           anisotropic Musielak–Orlicz spaces in absence of Lavrentiev's phenomenon
           
    • Abstract: Publication date: Available online 19 February 2019Source: Journal of Differential EquationsAuthor(s): Iwona Chlebicka, Piotr Gwiazda, Anna Zatorska-GoldsteinAbstractThe paper concerns existence and uniqueness of solutions to a nonlinear parabolic equation with merely integrable data on a Lipschitz bounded domain in RN. Our focal point is to involve the leading, nonlinear part of the operator whose growth is described by anisotropic N-function M inhomogeneous in the space and the time variables. The main goals are proven in absence of Lavrentiev's phenomenon, to ensure which we impose a certain type of balance of interplay between the behavior of M for large ξ and small changes of time and space variables. Its instances are log-Hölder continuity of variable exponent (inhomogeneous in time and space) or optimal closeness condition for powers in double phase spaces (possibly changing in time). New delicate approximation-in-time result is proven and applied in the construction of renormalized solutions.
       
  • New singular standing wave solutions of the nonlinear Schrodinger equation
    • Abstract: Publication date: Available online 14 February 2019Source: Journal of Differential EquationsAuthor(s): W.C. TroyAbstractWe prove existence, and asymptotic behavior as r→∞, of a family of singular solutions of(1)y″+2ry′+y y p−1−y=0,0
       
  • Nonlinear Schrödinger equation in the Bopp–Podolsky electrodynamics:
           Solutions in the electrostatic case
    • Abstract: Publication date: Available online 14 February 2019Source: Journal of Differential EquationsAuthor(s): Pietro d'Avenia, Gaetano SicilianoAbstractWe study the following nonlinear Schrödinger–Bopp–Podolsky system{−Δu+ωu+q2ϕu= u p−2u−Δϕ+a2Δ2ϕ=4πu2 inR3 with a,ω>0. We prove existence and nonexistence results depending on the parameters q,p. Moreover we also show that, in the radial case, the solutions we find tend to solutions of the classical Schrödinger–Poisson system as a→0.
       
  • Global well-posedness of the free-surface incompressible Euler equations
           with damping
    • Abstract: Publication date: Available online 14 February 2019Source: Journal of Differential EquationsAuthor(s): Jiali LianAbstractWe consider a layer of an incompressible inviscid fluid, bounded below by a fixed solid boundary and above by a free moving boundary, in a horizontally periodic setting. The fluid dynamics is governed by the gravity-driven incompressible Euler equations with damping, and the effect of surface tension is neglected on the free surface. We prove that the problem is globally well-posed for the small initial data and that solutions decay to the equilibrium at an almost exponential rate.
       
  • High order Melnikov method: Theory and application
    • Abstract: Publication date: Available online 14 February 2019Source: Journal of Differential EquationsAuthor(s): Fengjuan Chen, Qiudong WangAbstractLet D(t0,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t0,ε) as a formal power series in ε asD(t0,ε)=E0(t0)+εE1(t0)+⋯+εnEn(t0)+⋯. In this paper we derive an explicit integral formula for E1(t0). We also evaluate E1(t0) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.
       
  • Blow-up phenomena for linearly perturbed Yamabe problem on manifolds with
           umbilic boundary
    • Abstract: Publication date: Available online 12 February 2019Source: Journal of Differential EquationsAuthor(s): Marco Ghimenti, Anna Maria Micheletti, Angela PistoiaAbstractWe build blowing-up solutions for linear perturbation of the Yamabe problem on manifolds with umbilic boundary, provided the Weyl tensor is nonzero everywhere on the boundary and the dimension of the manifold is n≥11.
       
  • Existence for a k-Hessian equation involving supercritical growth
    • Abstract: Publication date: Available online 12 February 2019Source: Journal of Differential EquationsAuthor(s): José Francisco de Oliveira, João Marcos do Ó, Pedro UbillaAbstractIn this paper we use variational techniques to give existence results for the problem{Sk[u]=f(x,−u)inΩu
       
  • Boundary layers for the subcritical modes of the 3D primitive equations in
           a cube
    • Abstract: Publication date: Available online 6 February 2019Source: Journal of Differential EquationsAuthor(s): Makram Hamouda, Daozhi Han, Chang-Yeol Jung, Krutika Tawri, Roger TemamAbstractIn this article we study the boundary layers for the subcritical modes of the viscous Linearized Primitive Equations (LPEs) in a cube at small viscosity. The boundary layers include the parabolic boundary layers, ordinary boundary layers, and their interaction-corner layers. The boundary layer correctors are determined by a phenomenological study reminiscent of the Prandtl corrector approach and then a rigorous convergence result is proved which a posteriori justifies the phenomenological study.
       
  • Wong–Zakai approximation for the stochastic
           Landau–Lifshitz–Gilbert equations
    • Abstract: Publication date: Available online 5 February 2019Source: Journal of Differential EquationsAuthor(s): Zdzisław Brzeźniak, Utpal Manna, Debopriya MukherjeeAbstractIn this work we study stochastic Landau–Lifshitz–Gilbert equations (SLLGEs) in one dimension, with non-zero exchange energy only. Firstly, by introducing a suitable transformation, we convert the SLLGEs to a highly nonlinear time dependent partial differential equation with random coefficients, which is not fully parabolic. We then prove that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal regularity property. Following regular approximation of the Brownian motion and using reverse transformation, we show existence of strong solution of SLLGEs taking values in a two-dimensional unit sphere S2 in R3. The construction of the solution and its corresponding convergence results are based on Wong–Zakai approximation.
       
  • Existence and regularity of the solutions of some singular
           Monge–Ampère equations
    • Abstract: Publication date: Available online 1 February 2019Source: Journal of Differential EquationsAuthor(s): Haodi Chen, Genggeng HuangAbstractIn this paper, we investigate the following singular Monge–Ampère equation(0.1){det⁡D2u=1(Hu)n+k+2u⁎kinΩ⊂⊂Rn,u=0,on∂Ω where k≥0, H
       
  • Global existence and boundedness of solutions to a chemotaxis system with
           singular sensitivity and logistic-type source
    • Abstract: Publication date: Available online 1 February 2019Source: Journal of Differential EquationsAuthor(s): Xiangdong Zhao, Sining ZhengAbstractWe consider the fully parabolic Keller–Segel system with singular sensitivity and logistic-type source: ut=Δu−χ∇⋅(uv∇v)+ru−μuk, vt=Δv−v+u under the non-flux boundary conditions in a smooth bounded convex domain Ω⊂Rn, χ,r,μ>0, k>1. A global very weak solution for the system with n≥2 is obtained under one of the following conditions: (i) r>χ24 for 0max⁡{χ24(1−p02),χ−1} for χ>2 with p0=4(k−1)4+(2−k)kχ2 if k∈(2−1n,2]; (ii) χ22. Furthermore, this global very weak solution should be globally bounded in fact provided rμ and the initial data ‖u0‖L2(Ω),‖
       
 
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