Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle
type: Item
instance of: scholarly article
title: Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle
zbMATH Open document ID: 1064.35076
author: B. Fiedler
author: C. Rocha
author: Matthias Wolfrum
published in: Journal of Differential Equations
publication date: 2004-10-01T00:00:00Z
review text: The authors investigate scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions in one space dimension. The translational invariance generates so-called rotating wave solutions which are periodic in space and time. The authors use zero number properties of the solutions to establish necessary and sufficient conditions for the existence of heteroclinic orbits, connecting rotating waves at time \(\pm\infty\). The results give a complete combinatorial description of the attractor of this parabolic equation under suitable dissipativity assumptions.
reviewed by: Arnd Scheel
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 2104528
zbMATH Keywords: reaction-advection-diffusion equations
zbMATH Keywords: one space dimension
zbMATH Keywords: zero number properties
zbMATH Keywords: complete combinatorial description of the attractor
MaRDI profile type: Publication
full work available at URL: j.jde.2003.10.027
OpenAlex ID: W2060613029
Wikidata QID: Q60143396
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DOI: 10.1016/J.JDE.2003.10.027
description: scientific article; zbMATH DE number 2104528