Multiple spreading phenomena for a free boundary problem of a reaction-diffusion equation with a certain class of bistable nonlinearity

Yusuke Kawai, Yoshio Yamada

    Research output: Contribution to journalArticle

    17 Citations (Scopus)

    Abstract

    This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.

    Original languageEnglish
    Pages (from-to)538-572
    Number of pages35
    JournalJournal of Differential Equations
    Volume261
    Issue number1
    DOIs
    Publication statusPublished - 2016 Jul 5

    Keywords

    • Comparison theorem
    • Free boundary problem
    • Reaction-diffusion equation
    • Semi-wave
    • Spreading
    • Vanishing

    ASJC Scopus subject areas

    • Analysis

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