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doi: 10.3934/era.2021024

## Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect

 School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 611756, China

* Corresponding author: Bang-Sheng Han

Received  December 2020 Revised  February 2021 Published  March 2021

Fund Project: The second author is supported by NSF grant11801470 and the Fundamental Research Funds for the Central Universities (2682018CX64)

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.

Citation: Meng-Xue Chang, Bang-Sheng Han, Xiao-Ming Fan. Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect. Electronic Research Archive, doi: 10.3934/era.2021024
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