Subjects -> MATHEMATICS (Total: 1108 journals)
    - APPLIED MATHEMATICS (89 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (815 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (25 journals)
    - PROBABILITIES AND MATH STATISTICS (111 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: 71)
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: 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: 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: 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: 1)
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: 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: 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: 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)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 5)
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: 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  
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: 2)
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: 4)
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: 2)
Mathematics Education Research Journal     Partially Free   (Followers: 18)
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: 5)
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)

  First | 1 2 3 4 5     

Similar Journals
Journal Cover
Journal of Evolution Equations
Journal Prestige (SJR): 1.588
Citation Impact (citeScore): 1
Number of Followers: 0  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1424-3202 - ISSN (Online) 1424-3199
Published by Springer-Verlag Homepage  [2626 journals]
  • Self-similar asymptotics for solutions to the intermediate long-wave
           equation
    • Abstract: We consider the Cauchy problem for the intermediate long-wave equation $$\begin{aligned} u_{t}-\partial _{x}u^{2}+\frac{1}{\vartheta }u_{x}+VP\int _{\mathbb {R}}\frac{1}{2\vartheta }\coth \left( \frac{\pi \left( y-x\right) }{2\vartheta }\right) u_{yy}\left( t,y\right) \mathrm{d}y=0, \end{aligned}$$ where \(\vartheta >0\) . Our purpose in this paper is to prove the large time asymptotic behavior of solutions under the nonzero mass condition \(\int u_{0}\left( x\right) \mathrm{d}x\ne 0\) .
      PubDate: 2019-03-22
      DOI: 10.1007/s00028-019-00498-5
       
  • Existence of weak solutions for the nonlocal energy-weighted fractional
           reaction–diffusion equations
    • Abstract: For any bounded smooth domain \(\Omega \subset \mathbb {R}^n\) , we establish the global existence of weak solutions \(u\in L^2(0,T;H^s_{\Omega ,0})\) with \(u_t\in L^2(0,T;H^{-s}_{\Omega })\) to the initial boundary value problem of the nonlocal energy-weighted fractional reaction–diffusion equations for any initial data \(u_0\in H^s_{\Omega ,0}\) .
      PubDate: 2019-03-08
      DOI: 10.1007/s00028-019-00494-9
       
  • Anisotropic Sobolev embeddings and the speed of propagation for parabolic
           equations
    • Abstract: We consider a quasilinear parabolic Cauchy problem with spatial anisotropy of orthotropic type and study the spatial localization of solutions. Assuming that the initial datum is localized with respect to a coordinate having slow diffusion rate, we bound the corresponding directional velocity of the support along the flow. The expansion rate is shown to be optimal for large times.
      PubDate: 2019-03-07
      DOI: 10.1007/s00028-019-00493-w
       
  • Schauder bases and the decay rate of the heat equation
    • Abstract: We consider the classical Cauchy problem for the linear heat equation and integrable initial data in the Euclidean space \({\mathbb {R}}^N\) . We show that given a weighted \(L^p\) -space \(L_w^p({\mathbb {R}}^N)\) with \(1 \le p < \infty \) and a fast-growing weight w, there are Schauder bases \((e_n)_{n=1}^\infty \) in \(L_ w^p({\mathbb {R}}^N)\) with the following property: given a positive integer m, there exists \(n_m > 0\) such that, if the initial data f belong to the closed linear space of \(e_n\) with \(n \ge n_m\) , then the decay rate of the solution of the heat equation is at least \(t^{-m}\) . Such a basis can be constructed as a perturbation of any given Schauder basis. The proof is based on a construction of a basis of \(L_w^p( {\mathbb {R}}^N)\) , which annihilates an infinite sequence of bounded functionals.
      PubDate: 2019-03-02
      DOI: 10.1007/s00028-019-00492-x
       
  • Heat kernel asymptotics of the subordinator and subordinate Brownian
           motion
    • Abstract: For a class of Laplace exponents, we consider the transition density of the subordinator and the heat kernel of the corresponding subordinate Brownian motion. We derive explicit approximate expressions for these objects in the form of asymptotic expansions: via the saddle point method for the subordinator’s transition density and via the Mellin transform for the subordinate heat kernel. The latter builds on ideas from index theory using zeta functions. In either case, we highlight the role played by the analyticity of the Laplace exponent for the qualitative properties of the asymptotics.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0468-9
       
  • Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions
    • Abstract: Let \(\Omega \) be a bounded open subset with \(C^{1+\kappa }\) -boundary for some \(\kappa > 0\) . Consider the Dirichlet-to-Neumann operator associated with the elliptic operator \(- \sum \partial _l ( c_{kl} \, \partial _k ) + V\) , where the \(c_{kl} = c_{lk}\) are Hölder continuous and \(V \in L_\infty (\Omega )\) are real valued. We prove that the Dirichlet-to-Neumann operator generates a \(C_0\) -semigroup on the space \(C(\partial \Omega )\) which is in addition holomorphic with angle \(\frac{\pi }{2}\) . We also show that the kernel of the semigroup has Poisson bounds on the complex right half-plane. As a consequence, we obtain an optimal holomorphic functional calculus and maximal regularity on \(L_p(\Gamma )\) for all \(p \in (1,\infty )\) .
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0467-x
       
  • Supercaloric functions for the porous medium equation
    • Abstract: In the slow diffusion case, unbounded supersolutions of the porous medium equation are of two totally different types, depending on whether the pressure is locally integrable or not. This criterion and its consequences are discussed.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0474-y
       
  • Well-posedness for a pseudomonotone evolution problem with multiplicative
           noise
    • Abstract: Our aim is the study of well-posedness for the stochastic evolution equation $$\begin{aligned} \mathrm{d}u -\mathrm {div}\,( \nabla u ^{p-2}\nabla u +F(u)) \,\mathrm{d} t = H(u) \,\mathrm{d}W, \end{aligned}$$ for \(T>0\) , on a bounded Lipschitz domain \(D \subset \mathbb {R}^d\) with homogeneous Dirichlet boundary conditions, initial values \(u_0\in L^2(D)\) , \(p>2\) and \(F:\mathbb {R}\rightarrow \mathbb {R}^d\) Lipschitz continuous. W(t) is a cylindrical Wiener process in \(L^2(D)\) with respect to a filtration \((\mathcal {F}_t)\) satisfying the usual assumptions on a complete, countably generated probability space \((\varOmega ,\mathcal {F},\mathbb {P})\) . We consider the case of multiplicative noise satisfying appropriate regularity conditions. By a semi-implicit time discretization, we obtain approximate solutions. Using the theorems of Skorokhod and Prokhorov, we are able to pass to the limit and show existence of martingale solutions. We establish pathwise \(L^1\) -contraction and uniqueness and obtain existence and uniqueness of strong solutions.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0472-0
       
  • Existence to nonlinear parabolic problems with unbounded weights
    • Abstract: We consider the weighted parabolic problem of the type $$\begin{aligned} \begin{aligned} \left\{ \begin{array}{ll} u_t-\mathrm{div}(\omega _2(x) \nabla u ^{p-2} \nabla u )= \lambda \omega _1(x) u ^{p-2}u,&{} x\in \Omega ,\\ u(x,0)=f(x),&{} x\in \Omega ,\\ u(x,t)=0,&{} x\in \partial \Omega ,\ t>0,\\ \end{array}\right. \end{aligned} \end{aligned}$$ for quite a general class of possibly unbounded weights \( \omega _1,\omega _2\) satisfying the Hardy-type inequality. We prove existence of a global weak solution in the weighted Sobolev spaces provided that \(\lambda >0\) is smaller than the optimal constant in the inequality. The domain is assumed to be bounded or quasibounded. The obtained solution is proven to belong to $$\begin{aligned} L^p({{\mathbb {R}}}_+; W_{(\omega _1,\omega _2),0}^{1,p}(\Omega ))\cap L^\infty ({{\mathbb {R}}}_+; L^2(\Omega )). \end{aligned}$$
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0465-z
       
  • Blowing up radial solutions in the minimal Keller–Segel model of
           chemotaxis
    • Abstract: We consider the simplest parabolic–elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the blowup of radially symmetric solutions in terms of suitable Morrey spaces norms are derived.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0469-8
       
  • Well-posedness of systems of 1-D hyperbolic partial differential equations
    • Abstract: We consider the well-posedness of a class of hyperbolic partial differential equations on a one-dimensional spatial domain. This class includes in particular infinite networks of transport, wave and beam equations, or even combinations of these. Equivalent conditions for contraction semigroup generation are derived. We consider these equations on a finite interval as well as on a semi-axis.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0470-2
       
  • Global well-posedness and blow-up solutions of the Cauchy problem for a
           time-fractional superdiffusion equation
    • Abstract: We study the following time-fractional nonlinear superdiffusion equation $$\begin{aligned} \left\{ \begin{array}{l} {}_0^CD_t^\alpha u-\triangle u= u ^{p}, \ \ x\in \mathbb {R}^N,\ \ t>0, \\ u(0,x)=u_0(x),\ \ u_t(0,x)=u_1(x),\ \ x\in \mathbb {R}^N, \end{array}\right. \end{aligned}$$ where \(1<\alpha <2\) , \(p>1\) , \(u_0,u_1\in L^q(\mathbb {R}^N)\) ( \(q>1\) ) and \({_0^CD_t^\alpha u}\) denotes the Caputo fractional derivative of order \(\alpha .\) The critical exponents of this problem are determined when \(u_1\equiv 0\) and \(u_1\not \equiv 0, \) respectively.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0475-x
       
  • On the Navier–Stokes equation perturbed by rough transport noise
    • Abstract: We consider the Navier–Stokes system in two and three space dimensions perturbed by transport noise and subject to periodic boundary conditions. The noise arises from perturbing the advecting velocity field by space–time-dependent noise that is smooth in space and rough in time. We study the system within the framework of rough path theory and, in particular, the recently developed theory of unbounded rough drivers. We introduce an intrinsic notion of a weak solution of the Navier–Stokes system, establish suitable a priori estimates and prove existence. In two dimensions, we prove that the solution is unique and stable with respect to the driving noise.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0473-z
       
  • Topologies and measures on the space of functions of bounded variation
           taking values in a Banach or metric space
    • Abstract: We study functions of bounded variation with values in a Banach or in a metric space. In finite dimensions, there are three well-known topologies; we argue that in infinite dimensions there is a natural fourth topology. We provide some insight into the structure of these four topologies. In particular, we study the meaning of convergence, duality and regularity for these topologies and provide some useful compactness criteria, also related to the classical Aubin–Lions theorem. After this we study the Borel \(\sigma \) -algebras induced by these topologies, and we provide some results about probability measures on the space of functions of bounded variation, which can be used to study stochastic processes of bounded variation.
      PubDate: 2019-03-01
      DOI: 10.1007/s00028-018-0471-1
       
  • Gradient estimates for perturbed Ornstein–Uhlenbeck semigroups on
           infinite-dimensional convex domains
    • Abstract: Let X be a separable Hilbert space endowed with a non-degenerate centred Gaussian measure \(\gamma \) , and let \(\lambda _1\) be the maximum eigenvalue of the covariance operator associated with \(\gamma \) . The associated Cameron–Martin space is denoted by H. For a sufficiently regular convex function \(U:X\rightarrow {{\mathbb {R}}}\) and a convex set \(\Omega \subseteq X\) , we set \(\nu :=\hbox {e}^{-U}\gamma \) and we consider the semigroup \((T_\Omega (t))_{t\ge 0}\) generated by the self-adjoint operator defined via the quadratic form $$\begin{aligned} (\varphi ,\psi )\mapsto \int _\Omega {\left\langle D_H\varphi ,D_H\psi \right\rangle }_H \hbox {d}\nu , \end{aligned}$$ where \(\varphi ,\psi \) belong to \(D^{1,2}(\Omega ,\nu )\) , the Sobolev space defined as the domain of the closure in \(L^2(\Omega ,\nu )\) of \(D_H\) , the gradient operator along the directions of H. A suitable approximation procedure allows us to prove some pointwise gradient estimates for \((T_{\Omega }(t))_{t\ge 0}\) . In particular, we show that $$\begin{aligned} D_H T_{\Omega }(t)f _H^p\le \hbox {e}^{- p \lambda _1^{-1} t}(T_{\Omega }(t) D_H f ^p_H), \quad \, t>0,\ \nu \text {-a.e. in }{\Omega }, \end{aligned}$$ for any \(p\in [1,+\infty )\) and \(f\in D^{1,p}({\Omega },\nu )\) . We deduce some relevant consequences of the previous estimate, such as the logarithmic Sobolev inequality and the Poincaré inequality in \({\Omega }\) for the measure \(\nu \) and some improving summability properties for \((T_\Omega (t))_{t\ge 0}\) . In addition, we prove that if f belongs to \(L^p(\Omega ,\nu )\) for some \(p\in (1,\infty )\) , then $$\begin{aligned} D_H T_\Omega (t)f ^p_H \le K_p t^{-\frac{p}{2}} T_\Omega (t) f ^p,\quad \, t>0,\ \nu \text {-a.e. in }\Omega , \end{aligned}$$ where \(K_p\) is a positive constant depending only on p. Finally, we investigate on the asymptotic behaviour of the semigroup \((T_{\Omega }(t))_{t\ge 0}\) as t goes to infinity.
      PubDate: 2019-02-22
      DOI: 10.1007/s00028-019-00491-y
       
  • On the $$L^p$$ L p – $$L^q$$ L q estimates of the gradient of solutions
           to the Stokes problem
    • Abstract: This paper is concerned with estimates of the gradient of the solutions to the Stokes IBVP both in a bounded and in an exterior domain. More precisely, we look for estimates of the kind \( \nabla v(t) _q \le g(t) \nabla v_0 _p,\;q\ge p>1,\) for all \(t>0\) , where function g is independent of v.
      PubDate: 2019-02-12
      DOI: 10.1007/s00028-019-00490-z
       
  • Degenerate Kirchhoff-type wave problems involving the fractional Laplacian
           with nonlinear damping and source terms
    • Abstract: In this paper, we consider the following Kirchhoff-type wave problems, with nonlinear damping and source terms involving the fractional Laplacian, $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} u_{tt} +[u]^{2\gamma -2}_{s}(-\Delta )^su+ u_t ^{a-2}u_t+u= u ^{b-2}u,\ &{}\text{ in } \Omega \times {\mathbb {R}}^{+}, \\ u(\cdot ,0)=u_0,\ \ \ \ u_t(\cdot ,0)=u_1,&{} \text{ in } \Omega ,\\ u=0,&{} \text{ in } ({\mathbb {R}}^N{\setminus } \Omega )\times {\mathbb {R}}^{+}_0, \end{array} \right. \end{aligned}$$ where \((-\Delta )^s\) is the fractional Laplacian, \([u]_{s}\) is the Gagliardo semi-norm of u, \(s\in (0,1)\) , \(2<a<2\gamma<b<2_s^*=2N/(N-2s)\) , \(\Omega \subset {\mathbb {R}}^N\) is a bounded domain with Lipschitz boundary \(\partial \Omega \) . Under some natural assumptions, we obtain the global existence, vacuum isolating, asymptotic behavior and blowup of solutions for the problem above by combining the Galerkin method with potential wells theory. The significant feature and difficulty of the problem are that the coefficient of \((-\Delta )^s\) can vanish at zero.
      PubDate: 2019-02-12
      DOI: 10.1007/s00028-019-00489-6
       
  • Optimal decay rates for the abstract viscoelastic equation
    • Abstract: In this paper, we consider an abstract viscoelastic equation with minimal conditions on the \(L^{1}(0,\infty )\) relaxation function g namely \( g^{\prime }(t)\le -\xi (t)H(g(t))\) , where H is an increasing and convex function near the origin and \(\xi \) is a nonincreasing function. With only these very general assumptions on the behavior of g at infinity, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial rates when \(H(s)=s^{p}\) and p covers the full admissible range [1, 2). We get the best decay rates expected under this level of generality and our new results substantially improve several earlier related results in the literature.
      PubDate: 2019-02-08
      DOI: 10.1007/s00028-019-00488-7
       
  • Probabilistic representation formula for the solution of fractional
           high-order heat-type equations
    • Abstract: We propose a probabilistic construction for the solution of a general class of fractional high-order heat-type equations in the one-dimensional case, by using a sequence of random walks in the complex plane with a suitable scaling. A time change governed by a class of subordinated processes allows to handle the fractional part of the derivative in space. We first consider evolution equations with space fractional derivatives of any order, and later we show the extension to equations with time fractional derivative (in the sense of Caputo derivative) of order \(\alpha \in (0,1)\) .
      PubDate: 2019-02-02
      DOI: 10.1007/s00028-019-00485-w
       
  • A note on singularities in finite time for the $$L^{2}$$ L 2 gradient flow
           of the Helfrich functional
    • Abstract: This work investigates the formation of singularities under the steepest descent \(L^2\) -gradient flow of \({{\,\mathrm{{ W}}\,}}_{\lambda _1, \lambda _2}\) with zero spontaneous curvature, i.e., the sum of the Willmore energy, \(\lambda _1\) times the area, and \(\lambda _2\) times the signed volume of an immersed closed surface without boundary in \(\mathbb {R}^3\) . We show that in the case that \(\lambda _1>1\) and \(\lambda _2=0\) , any immersion develops singularities in finite time under this flow. If \(\lambda _1 >0\) and \(\lambda _2 > 0\) , embedded closed surfaces with energy less than $$\begin{aligned} 8\pi +\min \left\{ \left( 16 \pi \lambda _1^3\right) \bigg /\left( 3\lambda _2^2\right) , 8\pi \right\} \end{aligned}$$ and positive volume evolve singularities in finite time. If in this case the initial surface is a topological sphere and the initial energy is less than \(8 \pi \) , the flow shrinks to a round point in finite time. We furthermore discuss similar results for the case that \(\lambda _2\) is negative. These results strengthen the ones of McCoy and Wheeler (Commun Anal Geom 24(4):843–886, 2016). For \(\lambda _1 >0\) and \(\lambda _2 \ge 0\) , they showed that embedded closed spheres with positive volume and energy close to \(4\pi \) , i.e., close to the Willmore energy of a round sphere, converge to round points in finite time.
      PubDate: 2019-02-01
      DOI: 10.1007/s00028-019-00483-y
       
 
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