Remarks on Spreading and Vanishing for Free Boundary Problems of Some Reaction-Diffusion Equations

DOI 4 Citations 7 References Open Access

Description

We discuss a free boundary problem for a diffusion equation in a one-dimensional interval which models the spreading of invasive or new species. Moreover, the free boundary represents a spreading front of the species and its dynamical behavior is determined by a Stefan-like condition. This problem has been proposed by Du and Lin (2010) and, recently, Kaneko and Yamada have studied a free boundary problem for a general reaction-diffusion equation under Dirichlet boundary conditions. The main purpose of this paper is to define "spreading" and "vanishing" of species for a free boundary problem with general nonlinearity and study the underlying principle to determine the spreading or vanishing behavior as time tends to infinity. It will be proved that vanishing occurs if and only if the free boundary stays in a bounded interval, and that, when vanishing occurs, the population decreases exponentially to zero in large time.

Journal

  • Funkcialaj Ekvacioj

    Funkcialaj Ekvacioj 57 (3), 449-465, 2014

    Division of Functional Equations, The Mathematical Society of Japan

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Details 詳細情報について

  • CRID
    1390001205112580608
  • NII Article ID
    130004927737
  • DOI
    10.1619/fesi.57.449
  • ISSN
    05328721
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
    • CiNii Articles
    • KAKEN
    • OpenAIRE
  • Abstract License Flag
    Disallowed

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