Results 141 to 150 of about 1,252,466 (233)
Behavior of Solutions to Nonlocal Hyperbolic Diffusion and Doubly Nonlocal Cahn-Hilliard Equations
, 2018 This work focuses on two different type of nonlocal equations, the nonlocal diffusion equation and douby nonlocal Cahn-Hilliard equation. Nonlocal diffusion equation was introduced to model diffusive behavior when Fick’s law is not applicable.
White, Laura M
core
Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions
, 2009 We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly rescaled nonlocal problems approximate uniformly the solution of the corresponding Dirichlet problem for the ...
Manuel Elgueta +5 more
core +1 more source
Electronic Journal of Differential Equations, 2014 This article concerns the traveling wave solutions of nonlocal delay reaction-diffusion equations without local quasimonotonicity. The existence of traveling wave solutions is obtained by constructing upper-lower solutions and passing to a limit ...
Shuxia Pan
doaj
Physics-Informed Neural Network Modeling of Nonlocal Crowd Dynamics for Evacuation Scenarios
East European Journal of PhysicsWe investigate a nonlocal continuum model of crowd dynamics using a physics-informed neural network approach. The crowd is described by a system of nonlinear conservation laws in which the flux incorporates advection, diffusion, and nonlocal interaction
A. Naumovets +3 more
doaj +1 more source
Some nonlinear nonlocal elliptic problems under weak conditions on the diffusion coefficients
summary:Under weak conditions on the diffusion coefficients, we prove existence theorems of weak solutions for some nonlinear nonlocal elliptic problems.
Souilah, Rezak +2 more
core +1 more source
Nonlocal initial boundary value problem for the time-fractional diffusion equation
Electronic Journal of Differential Equations, 2017 In this article we discuss a method for constructing trace formulae for the heat-volume potential of the time-fractional diffusion equation to lateral surfaces of cylindrical domains and use these conditions to construct as well as to study a nonlocal
Makhmud Sadybekov, Gulaiym Oralsyn
doaj
Maximum principles, sliding techniques and applications to nonlocal equations
Electronic Journal of Differential Equations, 2007 This paper is devoted to the study of maximum principles holding for some nonlocal diffusion operators defined in (half-) bounded domains and its applications to obtain qualitative behaviors of solutions of some nonlinear problems.
Jerome Coville
doaj
Harnack estimates for nonlocal drift-diffusion equations
A set of pointwise estimates are established for local solutions to nonlocal diffusion equations with a drift term. In particular, our Harnack estimates are the first ones for such equations, and our Hölder regularity refines certain known result in ...
Liao, Naian
core +2 more sources
Nonlocal approximation of an anisotropic cross-diffusion system [PDF]
Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems.
Dębiec, Tomasz, Schmidtchen, Markus
core +1 more source