Subjects -> MATHEMATICS (Total: 1119 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (822 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (25 journals)

MATHEMATICS (822 journals)            First | 1 2 3 4 5     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of Computer Engineering, System and Science (CESS)     Open Access  
Journal of Contemporary Mathematical Analysis     Hybrid Journal  
Journal of Cryptology     Hybrid Journal   (Followers: 5)
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: 14)
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: 3)
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: 5)
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: 3)
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 Statistics Studies     Open Access   (Followers: 3)
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 2)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 3)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access   (Followers: 6)
Journal of Metallurgy     Open Access   (Followers: 8)
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   (Followers: 1)
Journal of Numerical Mathematics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access   (Followers: 5)
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: 5)
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: 9)
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: 16)
Journal of Turbulence     Hybrid Journal   (Followers: 9)
Journal of Uncertainty Analysis and Applications     Open Access   (Followers: 1)
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 11)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 6)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access   (Followers: 2)
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: 6)
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: 23)
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  
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: 1)
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: 4)
Mathematics and Statistics     Open Access   (Followers: 5)
Mathematics Education Forum Chitwan     Open Access   (Followers: 2)
Mathematics Education Journal     Open Access   (Followers: 3)
Mathematics Education Research Journal     Partially Free   (Followers: 20)
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: 6)
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: 5)
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)
Metrology and Instruments / Метрологія та прилади     Open Access  
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: 5)
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: 2)
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)
North Carolina Journal of Mathematics and Statistics     Open Access  
North-Holland Mathematical Library     Full-text available via subscription   (Followers: 1)
North-Holland Mathematics Studies     Full-text available via subscription  

  First | 1 2 3 4 5     

Similar Journals
Journal Cover
Journal of Dynamics and Differential Equations
Journal Prestige (SJR): 1.208
Citation Impact (citeScore): 1
Number of Followers: 0  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9222 - ISSN (Online) 1040-7294
Published by Springer-Verlag Homepage  [2656 journals]
  • Ground State Solutions of Discrete Asymptotically Linear Schrödinger
           Equations with Bounded and Non-periodic Potentials
    • Abstract: We study the existence of ground state solutions for a class of discrete nonlinear Schrödinger equations with a sign-changing potential V that converges at infinity and a nonlinear term being asymptotically linear at infinity. The resulting problem engages two major difficulties: one is that the associated functional is strongly indefinite and the other is that, due to the convergency of V at infinity, the classical methods such as periodic translation technique and compact inclusion method cannot be employed directly to deal with the lack of compactness of the Cerami sequence. New techniques are developed in this work to overcome these two major difficulties. This enables us to establish the existence of a ground state solution and derive a necessary and sufficient condition for a special case. To the best of our knowledge, this is the first attempt in the literature on the existence of a ground state solution for the strongly indefinite problem under no periodicity condition on the bounded potential and the nonlinear term being asymptotically linear at infinity. Moreover, our conditions can also be used to significantly improve the well-known results of the corresponding continuous nonlinear Schrödinger equation.
      PubDate: 2019-03-12
      DOI: 10.1007/s10884-019-09743-4
  • Bifurcation Analysis for a Delayed Diffusive Logistic Population Model in
           the Advective Heterogeneous Environment
    • Abstract: In this paper, we investigate a delayed reaction–diffusion–advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady state and associated Hopf bifurcation are obtained. A weighted inner product associated with the advection rate is introduced to compute the normal forms, which is the main difference between Hopf bifurcation for delayed reaction–diffusion–advection model and that for delayed reaction–diffusion model. Moreover, we find that the spatial scale and advection can affect Hopf bifurcation in the heterogenous environment.
      PubDate: 2019-03-08
      DOI: 10.1007/s10884-019-09739-0
  • Global Asymptotic Behavior of a Multi-species Stochastic Chemostat Model
           with Discrete Delays
    • Abstract: We consider a model of multi-species competition in the chemostat that includes demographic stochasticity and discrete delays. We prove that for any given initial data, there exists a unique global positive solution for the stochastic delayed system. By employing the method of stochastic Lyapunov functionals, we determine the asymptotic behaviors of the stochastic solution and show that although the sample path fluctuate, it remains positive and the expected time average of the distance between the stochastic solution and the equilibrium of the associated deterministic delayed chemostat model is eventually small, i.e. we obtain an analogue of the competition exclusion principle when the noise intensities are relatively small. Numerical simulations are carried out to illustrate our theoretical results.
      PubDate: 2019-03-07
      DOI: 10.1007/s10884-019-09741-6
  • Positive Solutions of Elliptic Boundary Value Problems and Applications to
           Population Dynamics
    • Abstract: In this paper, we investigate the dynamics of population inhabiting a favorable environment surrounded by a region where survival is impossible. We use a parabolic partial differential equation with nonlinearity changing signs to describe the dynamics. By using a recent result on the existence of nonzero fixed point for r-nowhere normal-outward compact maps, we establish new results on existence of nonzero nonnegative or positive steady-state solutions of such boundary value problems. Additionally, we obtain the convergence of positive solutions of such parabolic boundary value problems in the Banach space \(C^1\) , which is different from the previous results that considered weak convergence or uniform convergence.
      PubDate: 2019-03-07
      DOI: 10.1007/s10884-019-09742-5
  • On Local Strong Solutions to the 2D Cauchy Problem of the Compressible
           Non-resistive Magnetohydrodynamic Equations with Vacuum
    • Abstract: This paper concerns the Cauchy problem of the compressible non-resistive magnetohydrodynamic equations on the whole two-dimensional space with vacuum as far field density. When the shear and the bulk viscosities are a positive constant and a power function of the density respectively, we prove that there exists a unique local strong solution provided the initial density and the initial magnetic field decay not too slow at infinity. In particular, there is no need to require any Cho–Choe–Kim type compatibility conditions.
      PubDate: 2019-03-06
      DOI: 10.1007/s10884-019-09740-7
  • Determining Nodes for the Damped Forced Periodic Korteweg-de Vries
    • Abstract: We show that solutions of the periodic KdV equations $$\begin{aligned} u_t+\gamma u +u_{xxx}+uu_x=f, \end{aligned}$$ are asymptotically determined by their values at three points. That is if there exists \(x_1,x_2,x_3\) such that \(0< x_3-x_2<<x_3-x_1<<1\) and $$\begin{aligned} \lim _{t\rightarrow +\infty } u_1(t,x_j)-u_2(t,x_j) =0, \; \mathrm{for} \; j=1,2,3, \end{aligned}$$ for two solutions \(u_1,u_2\) of the KdV equation above, then $$\begin{aligned} \lim _{t\rightarrow +\infty } u_1(t)-u_2(t) _{H^1}=0. \end{aligned}$$
      PubDate: 2019-02-26
      DOI: 10.1007/s10884-019-09737-2
  • Stable and Unstable Periodic Spiky Solutions for the Gray–Scott System
           and the Schnakenberg System
    • Abstract: The Hopf bifurcations for the classical Gray–Scott system and the Schnakenberg system in an one-dimensional interval are considered. For each system, the existence of time-periodic solutions near the Hopf bifurcation parameter for a boundary spike is rigorously proved by the classical Crandall–Rabinowitz theory. The criteria for the stability of limit cycles are determined and it is shown that the Hopf bifurcation is supercritical for the Schnakenberg system, and hence the bifurcating periodic solutions are linearly stable. For the Gray–Scott system, there is a critical feeding rate, when the feeding rate of the system is greater than this critical feeding rate, the Hopf bifurcation is supercritical which implies the bifurcating periodic solutions are linearly stable, while when the feeding rate is smaller than this critical feeding rate, the Hopf bifurcation is subcritical, implying the bifurcating periodic solutions are linearly unstable.
      PubDate: 2019-02-22
      DOI: 10.1007/s10884-019-09736-3
  • A KAM Theorem for Higher Dimensional Wave Equations Under Nonlocal
    • Abstract: In this paper, we prove an infinite dimensional KAM theorem. As an application, it is shown that there are many real-analytic small-amplitude linearly-stable quasi-periodic solutions for higher dimensional wave equation under nonlocal perturbation $$\begin{aligned} u_{tt}-\triangle u +M_\xi u +\left( \int _{\mathbb {T}^d} u^2 dx\right) u=0,\quad t\in \mathbb {R},\ x\in \mathbb {T}^d\ \end{aligned}$$ where \(M_\xi \) is a real Fourier multiplier.
      PubDate: 2019-02-22
      DOI: 10.1007/s10884-019-09738-1
  • On the Center-Focus Problem for a Family of High-Order Polynomial
           Differential Systems
    • Abstract: In this paper, we have solved the center-focus problem for a family of high-order polynomial differential systems. We give the sufficient and necessary conditions for the corresponding periodic differential equation to have a center and also show that this center is a CC-center.
      PubDate: 2019-02-21
      DOI: 10.1007/s10884-019-09735-4
  • Asymptotic Profiles of Solutions for Structural Damped Wave Equations
    • Abstract: In this paper, we obtain several asymptotic profiles of solutions to the Cauchy problem for structurally damped wave equations \(\partial _{t}^{2} u - \varDelta u + \nu (-\varDelta )^{\sigma } \partial _{t} u=0\) , where \(\nu >0\) and \(0< \sigma \le 1\) . Our result is the approximation formula of the solution by a constant multiple of a special function as \(t \rightarrow \infty \) , which states that the asymptotic profiles of the solutions are classified into 5 patterns depending on the values \(\nu \) and \(\sigma \) . Here we emphasize that our main interest of the paper is in the case \(\sigma \in (\frac{1}{2},1)\) .
      PubDate: 2019-02-11
      DOI: 10.1007/s10884-019-09731-8
  • On Multivalent Guiding Functions Method in the Periodic Problem for Random
           Differential Equations
    • Abstract: By applying the random topological degree theory we develop the methods of random multivalent guiding functions and use them for the study of periodic solutions for random differential equations in finite dimensional spaces.
      PubDate: 2019-02-11
      DOI: 10.1007/s10884-019-09734-5
  • Competition in Periodic Media: III—Existence and Stability of Segregated
           Periodic Coexistence States
    • Abstract: In this paper we consider a system of parabolic reaction–diffusion equations with strong competition and two related scalar reaction–diffusion equations. We show that in certain space periodic media with large periods, there exist periodic, non-constant, non-trivial, stable stationary states. We compare our results with already known results about the existence and nonexistence of such solutions. Finally, we provide ecological interpretations for these results.
      PubDate: 2019-02-11
      DOI: 10.1007/s10884-019-09732-7
  • On Conditions for Rate-induced Tipping in Multi-dimensional Dynamical
    • Abstract: The possibility of rate-induced tipping (R-tipping) away from an attracting fixed point has been thoroughly explored in 1-dimensional systems. In these systems, it is impossible to have R-tipping away from a path of quasi-stable equilibria that is forward basin stable (FBS), but R-tipping is guaranteed for paths that are non-FBS of a certain type. We will investigate whether these results carry over to multi-dimensional systems. In particular, we will show that the same conditions guaranteeing R-tipping in 1-dimension also guarantee R-tipping in higher dimensions; however, it is possible to have R-tipping away from a path that is FBS even in 2-dimensional systems. We will propose a different condition, forward inflowing stability (FIS), which we show is sufficient to prevent R-tipping in all dimensions. The condition, while natural, is difficult to verify in concrete examples. Monotone systems are a class for which FIS is implied by an easily verifiable condition. As a result, we see how the additional structure of these systems makes predicting the possibility of R-tipping straightforward in a fashion similar to 1-dimension. In particular, we will prove that the FBS and FIS conditions in monotone systems reduce to comparing the relative positions of equilibria over time. An example of a monotone system is given that demonstrates how these ideas are applied to determine exactly when R-tipping is possible.
      PubDate: 2019-02-11
      DOI: 10.1007/s10884-019-09730-9
  • Correction to: Sturm Attractors for Quasilinear Parabolic Equations with
           Singular Coefficients
    • Abstract: The original version of this article unfortunately contained a mistake in Eq. 1.4. The correct equation is given below.
      PubDate: 2019-02-06
      DOI: 10.1007/s10884-019-09728-3
  • Robustness of Hyperbolicity in Delay Equations
    • Abstract: We establish the robustness of the notion of an exponential dichotomy for a nonautonomous linear delay equation. We consider the general cases of equations satisfying the Carathéodory conditions and of noninvertible evolution families defined by the linear equations. The stable and unstable spaces of the perturbed equations are obtained as images of linear operators that in their turn are fixed points of appropriate contraction maps.
      PubDate: 2019-02-06
      DOI: 10.1007/s10884-019-09733-6
  • Hilbert’s ‘Monkey Saddle’ and Other Curiosities in the Equilibrium
           Problem of Three Point Particles on a Circle for Repulsive Power Law
    • Abstract: This article determines all possible (proper as well as pseudo) equilibrium arrangements under a repulsive power law force of three point particles on the unit circle. These are the critical points of the sum over the three (standardized) Riesz pair interaction terms, each given by \(V_s(r)= s^{-1}\left( r^{-s}-1 \right) \) when the real parameter \(s \ne 0\) , and by \(V_0(r) := \lim _{s\rightarrow 0}V_s(r) = -\ln r\) ; here, r is the chordal distance between the particles in the pair. The bifurcation diagram which exhibits all these equilibrium arrangements together as functions of s features three obvious “universal” equilibria, which do not depend on s, and two not-so-obvious continuous families of s-dependent non-universal isosceles triangular equilibria. The two continuous families of non-universal equilibria are disconnected, yet they bifurcate off of a common universal limiting equilibrium (the equilateral triangular configuration), at \(s=-4\) , where the graph of the total Riesz energy of the 3-particle configurations has the shape of a “monkey saddle.” In addition, one of the families of non-universal equilibria also bifurcates off of another universal equilibrium (the antipodal arrangement), at \(s=-2\) . While the bifurcation at \(s=-4\) is analytical, the one at \(s=-2\) is not. The bifurcation analysis presented here is intended to serve as template for the treatment of similar N-point equilibrium problems on \({\mathbb {S}}^d\) for small N.
      PubDate: 2019-01-30
      DOI: 10.1007/s10884-019-09729-2
  • Blow Up Profiles for a Quasilinear Reaction–Diffusion Equation with
           Weighted Reaction with Linear Growth
    • Abstract: We study the blow up profiles associated to the following second order reaction–diffusion equation with non-homogeneous reaction: $$\begin{aligned} \partial _tu=\partial _{xx}(u^m) + x ^{\sigma }u, \end{aligned}$$ with \(\sigma >0\) . Through this study, we show that the non-homogeneous coefficient \( x ^{\sigma }\) has a strong influence on the blow up behavior of the solutions. First of all, it follows that finite time blow up occurs for self-similar solutions u, a feature that does not appear in the well known autonomous case \(\sigma =0\) . Moreover, we show that there are three different types of blow up self-similar profiles, depending on whether the exponent \(\sigma \) is closer to zero or not. We also find an explicit blow up profile. The results show in particular that global blow up occurs when \(\sigma >0\) is sufficiently small, while for \(\sigma >0\) sufficiently large blow up occurs only at infinity, and we give prototypes of these phenomena in form of self-similar solutions with precise behavior. This work is a part of a larger program of understanding the influence of non-homogeneous weights on the blow up sets and rates.
      PubDate: 2019-01-14
      DOI: 10.1007/s10884-018-09727-w
  • A Small Solid Body with Large Density in a Planar Fluid is Negligible
    • Abstract: In this article, we consider a small rigid body moving in a viscous fluid filling the whole \(\mathbb R^2\) . We assume that the diameter of the rigid body goes to 0, that the initial velocity has bounded energy and that the density of the rigid body goes to infinity. We prove that the rigid body has no influence on the limit equation by showing convergence of the solutions towards a solution of the Navier–Stokes equations in the full plane \(\mathbb {R}^{2}\) .
      PubDate: 2019-01-07
      DOI: 10.1007/s10884-018-9718-3
  • The Behavior of Boundary Layer for the Compressible Planar MHD Equations
           at Small Shear Viscosity
    • Abstract: The vanishing shear viscosity limit to an initial-boundary value problem of planar MHD equations for compressible viscous heat-conducting fluids is justified and the convergence rates are obtained. More important, to capture the behavior of the solutions at small shear viscosity, both the boundary-layer thickness and the boundary-layer corrector are discussed.
      PubDate: 2019-01-04
      DOI: 10.1007/s10884-018-9726-3
  • On a Subclass of Solutions of the 2D Navier–Stokes Equations with
           Constant Energy and Enstrophy
    • Abstract: In this paper, we are interested in studying the existence of the nonstationary solutions in the global attractor of the 2D Navier–Stokes equations with constant energy and enstrophy. We particularly focus on a subclass of these solutions that the geometric structures have a supplementary stability property which were called “chained ghost solutions” in Tian and Zhang (Indiana Univ Math J 64:1925–1958, 2015). By solving a Galerkin system of a particular form, we show the nonexistence of the chained ghost solutions for certain cases.
      PubDate: 2019-01-02
      DOI: 10.1007/s10884-018-9721-8
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