Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations

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Abstract

For a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been well known. This paper proves that an axially asymmetric traveling front with any positive speed does exist in a balanced bistable reaction-diffusion equation. Our method is as follows. We use a pyramidal traveling front for an unbalanced reaction-diffusion equation whose cross section has a major axis and a minor axis. Preserving the ratio of the major axis and a minor axis to be a constant and taking the balanced limit, we obtain a traveling front in a balanced bistable reaction-diffusion equation. This traveling front is monotone decreasing with respect to the traveling axis, and its cross section is a compact set with a major axis and a minor axis when the constant ratio is not 1.

Original languageEnglish
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
DOIs
Publication statusPublished - Jan 1 2019

Keywords

  • Asymmetric
  • Balanced
  • Reaction-diffusion equation
  • Traveling front

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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