Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations

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    5 Citations (Scopus)

    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
    Pages (from-to)1791-1816
    Number of pages26
    JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
    Volume36
    Issue number7
    DOIs
    Publication statusPublished - Nov 1 2019

    Keywords

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

    ASJC Scopus subject areas

    • Analysis
    • Mathematical Physics
    • Applied Mathematics

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