Regular traveling waves for a nonlocal diffusion equation
type: Item
instance of: scholarly article
title: Regular traveling waves for a nonlocal diffusion equation
zbMATH Open document ID: 1323.35089
author: Zhaoquan Xu
author: Dongmei Xiao
published in: Journal of Differential Equations
publication date: 2014-10-27T00:00:00Z
review text: In this paper, the authors study a nonlocal diffusion equation with a general diffusion kernel and delayed non-linearity, and obtain the existence, nonexistence and uniqueness of the regular traveling wave solutions for this nonlocal diffusion equation. The existence of traveling wave solutions is proved by upper-lower solutions (large wave speed) and passing to a limit function (minimal wave speed). For both monotone and non-monotone cases, the uniqueness up to transition is investigated. As an application of the results, the authors reconsider some models arising from population dynamics, epidemiology and neural networks.
reviewed by: Guo Lin
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35R09
zbMATH DE Number: 6361739
zbMATH Keywords: regular traveling waves
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: nonlocal diffusion equations, delayed nonlinearity
MaRDI profile type: Publication
full work available at URL: j.jde.2014.09.008
OpenAlex ID: W2059300156
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DOI: 10.1016/J.JDE.2014.09.008
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description: scientific article; zbMATH DE number 6361739