Spreading and vanishing behaviors for radially symmetric solutions of free boundary problems for reaction-diffusion equations

Yuki Kaneko

    Research output: Contribution to journalArticle

    19 Citations (Scopus)


    We discuss free boundary problems modeling the diffusion of invasive or new species in a multi-dimensional ball or annulus, where unknown functions are population density and the outer boundary representing the spreading front of the species. We define spreading and vanishing to describe the asymptotic behaviors of radially symmetric solutions. The main purpose is to study the underlying principle to determine spreading and vanishing for the free boundary problems of general reaction-diffusion equations. We also focus on the problems with a logistic or bistable reaction term to show dichotomy results, vanishing speed and sufficient conditions for spreading or vanishing.

    Original languageEnglish
    Pages (from-to)121-140
    Number of pages20
    JournalNonlinear Analysis: Real World Applications
    Issue number1
    Publication statusPublished - 2014


    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Computational Mathematics
    • Engineering(all)
    • Medicine(all)
    • Economics, Econometrics and Finance(all)

    Cite this