Open AccessGlobal dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect
Author(s) -
Meng-Xue Chang,
Byungjin Han,
Xiaoming Fan
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021024
Subject(s) - bistability , reaction–diffusion system , bounded function , initial value problem , mathematics , diffusion , cauchy problem , mathematical analysis , dynamics (music) , physics , thermodynamics , quantum mechanics , acoustics
This paper is devoted to studying the Cauchy problem corresponding to the nonlocal bistable reaction diffusion equation. It is the first attempt to use the method of comparison principle to study the well-posedness for the nonlocal bistable reaction-diffusion equation. We show that the problem has a unique solution for any non-negative bounded initial value by using Gronwall's inequality. Moreover, the boundedness of the solution is obtained by means of the auxiliary problem. Finally, in the case that the initial data with compactly supported, we analyze the asymptotic behavior of the solution.