Almost planar waves in anisotropic media

Mariana Haragus, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We investigate corners and steps of interfaces in anisotropic systems. Starting from a stable planar front in a general reaction-diffusion-convection system, we show existence of almost planar interior and exterior corners. When the interface propagation is unstable in some directions, we show that small steps in the interface may persist. Our assumptions are based on physical properties of interfaces such as linear and nonlinear dispersion, rather than properties of the modeling equations-such as variational or comparison principles. We also give geometric criteria based on the Cahn-Hoffman vector, that distinguish between the formation of interior and exterior comers.

Original languageEnglish (US)
Pages (from-to)791-815
Number of pages25
JournalCommunications in Partial Differential Equations
Volume31
Issue number5
DOIs
StatePublished - May 2006

Bibliographical note

Funding Information:
This work was partially supported by the MRT through grant ACI JC 1039 (M. H.) and by the NSF through grants DMS-0203301 and DMS 0504271 (A. S.).

Keywords

  • Anisotropy
  • Burgers equation
  • Cahn-Hoffmann vector
  • Corners in interfaces

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