Corner defects in almost planar interface propagation

Mariana Haragus, Arnd Scheel

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52 Scopus citations

Abstract

We study existence and stability of interfaces in reaction-diffusion systems which are asymptotically planar. The problem of existence of corners is reduced to an ordinary differential equation that can be viewed as the travelling-wave equation to a viscous conservation law or variants of the Kuramoto-Sivashinsky equation. The corner typically, but not always, points in the direction opposite to the direction of propagation. For the existence and stability problem, we rely on a spatial dynamics formulation with an appropriate equivariant parameterization for relative equilibria.

Original languageEnglish (US)
Pages (from-to)283-329
Number of pages47
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume23
Issue number3
DOIs
StatePublished - 2006

Bibliographical note

Funding Information:
M. Haragus wishes to thank the School of Mathematics, University of Minnesota, for hospitality provided during the preparation of part of this paper. A. Scheel was partially supported by the NSF through grant DMS-0203301.

Keywords

  • Burgers equation
  • Interfaces
  • Kuramoto-Sivashinsky equation
  • Quadratic systems
  • Reaction-diffusion systems
  • Stability

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