Stability of travelling waves with noncritical speeds for double degenerate Fisher-type equations
type: Item
instance of: scholarly article
title: Stability of travelling waves with noncritical speeds for double degenerate Fisher-type equations
zbMATH Open document ID: 1170.35327
author: Yi Li
author: Yaping Wu
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2008-07-21T00:00:00Z
review text: This article focuses on a Fisher-type equation where the classical nonlinearity \(u\,(1-u)\) is replaced by \(u^p\,(1-u)^q\), \(p,q>1\). For this type of equation it is known that there exists a critical speed \(c^*\) such that there exist traveling wave solutions for any speed \(c\geq c^*\) connecting the solutions \(u=0\) and \(u=1\). Traveling waves with \(c>c^*\) are shown to be exponentially stable in certain exponentially weighted spaces and locally algebraically/exponentially stable in certain polynomially/exponentially weighted spaces.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A18
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5302656
zbMATH Keywords: asymptotic stability
zbMATH Keywords: traveling waves
zbMATH Keywords: algebraic decay
zbMATH Keywords: spectral analysis
zbMATH Keywords: semigroup methods
MaRDI profile type: Publication
full work available at URL: dcdsb.2008.10.149
OpenAlex ID: W2014200830
DOI: 10.3934/DCDSB.2008.10.149
description: scientific article; zbMATH DE number 5302656