Propagating interface in reaction-diffusion equations with distributed delay

Electronic Journal of Differential Equations

article

Haoyu Wang¹  Ge Tian² 

[1] School of Information Science and Engineering Lanzhou University Lanzhou;School of Mathematics and Statistics Lanzhou University Lanzhou

关键词: Reaction-diffusion equations;    distributed delay;    traveling wave;    propagating interface.;   

DOI  :  10.58997/ejde.2021.54

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

This article concerns the limiting behavior of the solution to a reaction-diffusionequation with distributed delay. We firstly consider the quasi-monotone situation andthen investigate the non-monotone situation by constructing two auxiliary quasi-monotoneequations. The limit behaviors of solutions of the equation can be obtained from thesandwich technique and the comparison principle of the Cauchy problem.It is proved that the propagation speed of the interface is equal to the minimum wavespeed of the corresponding traveling waves. This makes possible to observe theminimum speed of traveling waves from a new perspective.

【 授权许可】

CC BY