Nontrivial large-time behaviour in bistable reaction-diffusion equations
type: Item
instance of: scholarly article
title: Nontrivial large-time behaviour in bistable reaction-diffusion equations
zbMATH Open document ID: 1178.35074
author: J. M. Roquejoffre
author: Violaine Roussier-Michon
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2009-10-02T00:00:00Z
review text: Bistable reaction-diffusion equations are known to admit one-dimensional travelling waves which are globally stable to one-dimensional perturbations. These planar waves are also stable to two-dimensional perturbations. These perturbations decay in the direction transverse to the wave, in an integrable fashion. The authors first prove that this result breaks down when the integrability condition is removed and exhibit a large-time dynamics similar to that of the heat equation. This result is then applied to the study of the large-time behaviour of conical-shaped fronts in the plane and cases where the dynamics is given by that of two advection-diffusion equations are investigated.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 5610623
zbMATH Keywords: advection-diffusion equations
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: travelling fronts
zbMATH Keywords: nontrivial dynamics
reviewed by: J. Michel Tchuenche
MaRDI profile type: Publication
full work available at URL: s10231-008-0072-7
OpenAlex ID: W2076013429
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DOI: 10.1007/S10231-008-0072-7
description: scientific article; zbMATH DE number 5610623