Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation
type: Item
instance of: scholarly article
title: Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation
zbMATH Open document ID: 1113.35094
author: S. Kamin
author: P. Rosenau
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2006-09-28T00:00:00Z
review text: The authors study the problem \[ u_t=(u^m)_{xx} +u(1-u^{m-1}), \;x \in \mathbb R, \;t > 0, \;\;u(0,x)=u_0(x) \geq 0, \;x \in \mathbb R \] with \(m > 1\). If the initial datum \(u_0(x)\) decays fast enough at infinity, it is proved that the solution of the Cauchy problem approaches the travelling wave solution spreading either to the right or to the left, or two travelling waves moving in opposite directions. The proofs of some auxiliary lemmas are not included in the paper.
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5058758
zbMATH Keywords: Asymptotic behaviour of solutions
zbMATH Keywords: nonlinear diffusion
zbMATH Keywords: reaction-diffusion equation
zbMATH Keywords: traveling waves
reviewed by: Luis Alberto Fernández
MaRDI profile type: Publication
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description: scientific article