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)

    Abstract

    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
    Volume18
    Issue number1
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Radially Symmetric Solutions
    Free Boundary Problem
    Reaction-diffusion Equations
    Dichotomy
    Ring or annulus
    Population Density
    Logistics
    Ball
    Asymptotic Behavior
    Unknown
    Sufficient Conditions
    Term
    Modeling
    Free boundary problem
    Reaction-diffusion equations
    Population density
    Asymptotic behavior

    ASJC Scopus subject areas

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

    Cite this

    @article{6adfecbcb6b943639db47ce7d1cc3c0d,
    title = "Spreading and vanishing behaviors for radially symmetric solutions of free boundary problems for reaction-diffusion equations",
    abstract = "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.",
    author = "Yuki Kaneko",
    year = "2014",
    doi = "10.1016/j.nonrwa.2014.01.008",
    language = "English",
    volume = "18",
    pages = "121--140",
    journal = "Nonlinear Analysis: Real World Applications",
    issn = "1468-1218",
    publisher = "Elsevier BV",
    number = "1",

    }

    TY - JOUR

    T1 - Spreading and vanishing behaviors for radially symmetric solutions of free boundary problems for reaction-diffusion equations

    AU - Kaneko, Yuki

    PY - 2014

    Y1 - 2014

    N2 - 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.

    AB - 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.

    UR - http://www.scopus.com/inward/record.url?scp=84897983938&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84897983938&partnerID=8YFLogxK

    U2 - 10.1016/j.nonrwa.2014.01.008

    DO - 10.1016/j.nonrwa.2014.01.008

    M3 - Article

    AN - SCOPUS:84897983938

    VL - 18

    SP - 121

    EP - 140

    JO - Nonlinear Analysis: Real World Applications

    JF - Nonlinear Analysis: Real World Applications

    SN - 1468-1218

    IS - 1

    ER -