Corner defects in almost planar interface propagation

Mariana Haragus; Arnd Scheel

doi:10.1016/j.anihpc.2005.03.003

Corner defects in almost planar interface propagation

Mariana Haragus, Arnd Scheel

School of Mathematics

Research output: Contribution to journal › Article › peer-review

61 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 language	English (US)
Pages (from-to)	283-329
Number of pages	47
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	23
Issue number	3
DOIs	https://doi.org/10.1016/j.anihpc.2005.03.003
State	Published - 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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10.1016/j.anihpc.2005.03.003

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title = "Corner defects in almost planar interface propagation",

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.",

keywords = "Burgers equation, Interfaces, Kuramoto-Sivashinsky equation, Quadratic systems, Reaction-diffusion systems, Stability",

author = "Mariana Haragus and Arnd Scheel",

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.",

year = "2006",

doi = "10.1016/j.anihpc.2005.03.003",

language = "English (US)",

volume = "23",

pages = "283--329",

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TY - JOUR

T1 - Corner defects in almost planar interface propagation

AU - Haragus, Mariana

AU - Scheel, Arnd

N1 - 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.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Burgers equation

KW - Interfaces

KW - Kuramoto-Sivashinsky equation

KW - Quadratic systems

KW - Reaction-diffusion systems

KW - Stability

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VL - 23

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EP - 329

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

IS - 3

ER -

Corner defects in almost planar interface propagation

Abstract

Bibliographical note

Keywords

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