Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system
type: Item
instance of: scholarly article
title: Spatial dynamics of a nonlocal and time-delayed reaction-diffusion system
zbMATH Open document ID: 1180.35536
author: Jian Fang
author: Junjie Wei
author: Xiao-Qiang Zhao
published in: Journal of Differential Equations
publication date: 2008-11-12T00:00:00Z
review text: The goal of this paper is to study the asymptotic speed of spread, the existence and nonexistence of travelling wave for the following nonlocal and time-delayed reaction-diffusion system \[ \begin{cases}\frac {\partial u}{\partial t}= d\Delta u+d\int^T_0\int_\mathbb{R} F(s,y)u(t-s,x-y)dy\,ds-\beta u^2(t,x)\\ \frac {\partial v}{\partial t}=D\Delta v-\gamma v+ \alpha u-\alpha\int^T_0\int_\mathbb{R} F (s,y)u(t-s,x-y)dy\,ds,\end{cases} \tag{1} \] where \(\tau\in(0,\infty],d,D,\alpha,\beta, \gamma\) are positive and \(F:\mathbb{R}^2\to\mathbb{R}\) satisfies natural assumptions.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5365150
zbMATH Keywords: nonlocal reaction-diffusion system
zbMATH Keywords: time delay
zbMATH Keywords: spreading speed
zbMATH Keywords: traveling waves
zbMATH Keywords: minimal wave speed
MaRDI profile type: Publication
full work available at URL: j.jde.2008.09.001
OpenAlex ID: W2035426056
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DOI: 10.1016/J.JDE.2008.09.001
description: scientific article; zbMATH DE number 5365150