Coexistence of a pulse and multiple spikes and transition layers in the standing waves of a reaction-diffusion system
type: Item
instance of: scholarly article
title: Coexistence of a pulse and multiple spikes and transition layers in the standing waves of a reaction-diffusion system
zbMATH Open document ID: 1058.35112
author: Fu Zhang
published in: Journal of Differential Equations
publication date: 2004-11-22T00:00:00Z
review text: The author studies the existence of standing waves with one pulse and transition layer in the nonlinear reaction-diffusion system: \(u_{t}=f(u,w)+u_{xx}\), \(w_{t}= \varepsilon^{2}g(u,w)+ w_{xx}\), \(x\in \mathbb{R}\), where \(\varepsilon>0\) is a small parameter, \(f(u,w)\) has three branches \(u=h_{i}(w),\;i=1,2,3\) on an interval of \(w\) and \(g(u,w)=0\) intersects \(u=h_{1}(w)\) once and \(u=h_{3}(w)\) at most once. The method is a topological shooting plan consisting of various shooting arguments. The main technical advance of this plan is that it provides a setup for proving the existence of not only a single pulse, but also multiple spikes and transition layer.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B25
zbMATH DE Number: 2117238
zbMATH Keywords: standing waves
zbMATH Keywords: topological shooting plan
reviewed by: Jiaqi Mo
MaRDI profile type: Publication
full work available at URL: j.jde.2004.06.017
OpenAlex ID: W1988430989
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DOI: 10.1016/J.JDE.2004.06.017
description: scientific article; zbMATH DE number 2117238