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

被引：0

作者：

Croitoru, Anca ^{[1
]}

Tanase, Gabriela ^{[1
]}

机构：

[1] Alexandru Ioan Cuza Univ, Fac Math, Bd Carol I 11, Iasi 700506, Romania

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2022年

关键词：

Nonlinear reaction-diffusion problem of parabolic type; nonlocal dif-fusion; heat equation; qualitative properties of solutions; fixed point; in-homogeneous Neumann boundary conditions; finite difference scheme; FIELD TRANSITION SYSTEM; NONHOMOGENEOUS CAUCHY-NEUMANN; ITERATIVE SCHEME; WELL-POSEDNESS; GENERAL-CLASS; EQUATION; REGULARITY; UNIQUENESS; EXISTENCE;

D O I：

10.3934/dcdss.2022155

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the existence and uniqueness of the solution in C((0, T], L & INFIN;(omega)) 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.

引用

页码：75 / 88

页数：14

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