QUALITATIVE AND QUANTITATIVE ANALYSIS FOR A NONLOCAL AND NONLINEAR REACTION-DIFFUSION PROBLEM WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

COSTICA MOROSANU; BIANCA SATCO

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QUALITATIVE AND QUANTITATIVE ANALYSIS FOR A NONLOCAL AND NONLINEAR REACTION-DIFFUSION PROBLEM WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

机译：QUALITATIVE AND QUANTITATIVE ANALYSIS FOR A NONLOCAL AND NONLINEAR REACTION-DIFFUSION PROBLEM WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

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摘要

The main goal of this paper is to introduce and analyze a new nonlocal reaction-diffusion model with in-homogeneous Neumann boundary conditions. We prove the existence and uniqueness of a solution in the class C((0, T], L~∞(Ω)) and the dependence on the data. Proofs are based on the Banach fixed-point theorem. Our results extend the results already proven by other authors. A numerical approximating scheme and a series of numerical experiments are also presented in order to illustrate the effectiveness of the theoretical result. The overall scheme is explicit in time and does not need iterative steps; therefore it is fast.

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《Discrete and continuous dynamical systems, Series S》 |2023年第1期|1-15|共15页
作者
COSTICA MOROSANU; BIANCA SATCO;
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作者单位

Alexandru Ioan Cuza University - UAIC Bd. Carol I, No. 11, 700506, Iasi, Romania;

Faculty of Electrical Engineering and Computer Science Stefan cel Mare University of Suceava Universitatii 13, 720225, Suceava, 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; inhomogeneous Neumann boundary conditions; finite difference scheme;

QUALITATIVE AND QUANTITATIVE ANALYSIS FOR A NONLOCAL AND NONLINEAR REACTION-DIFFUSION PROBLEM WITH IN-HOMOGENEOUS NEUMANN BOUNDARY CONDITIONS

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