ON A NONLOCAL AND NONLINEAR SECOND-ORDER ANISOTROPIC REACTION-DIFFUSION MODEL WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

ANCA CROITORU; GABRIELA TANASE

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ON A NONLOCAL AND NONLINEAR SECOND-ORDER ANISOTROPIC REACTION-DIFFUSION MODEL WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

机译：ON A NONLOCAL AND NONLINEAR SECOND-ORDER ANISOTROPIC REACTION-DIFFUSION MODEL WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

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摘要

In this paper we study the existence and uniqueness of the solution in C((0, T, L~∞(Ω)) of a new nonlocal and nonlinear second-order anisotropic reaction-diffusion problem with in-homogeneous Neumann boundary conditions, generalizing other problems in the literature. Then, by using the finite difference method, we propose an explicit in time numerical scheme to approximate the unique solution of our problem. We also present some numerical simulations that come to show the performance of our theoretical model.

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《Discrete and continuous dynamical systems, Series S》 |2023年第1期|75-88|共14页
作者
ANCA CROITORU; GABRIELA TANASE;
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Faculty of Mathematics, University of Iasi Bd. Carol I, No. 11, 700506, Iasi, Romania;

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正文语种英语
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Nonlinear reaction-diffusion problem of parabolic type; nonlocal diffusion; heat equation; qualitative properties of solutions; fixed point; in-homogeneous Neumann boundary conditions; finite difference scheme;

ON A NONLOCAL AND NONLINEAR SECOND-ORDER ANISOTROPIC REACTION-DIFFUSION MODEL WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

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