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

Yusuke Kawai, Yoshio Yamada

    研究成果: Article査読

    19 被引用数 (Scopus)

    抄録

    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.

    本文言語English
    ページ(範囲)538-572
    ページ数35
    ジャーナルJournal of Differential Equations
    261
    1
    DOI
    出版ステータスPublished - 2016 7 5

    ASJC Scopus subject areas

    • Analysis

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