Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system

Kenji Nishihara

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is p= with p, q ≥ 1, pq > 1. When p, q satisfy max ((p+1)/(pq - 1), (q + 1)/(pq -1)) < N/2, the exponents p, q are supercritical. In this paper we assort the supercritical exponent case to two cases. In one case both p and q are bigger than the Fujita exponent ρF (N) = 1+2/N, while in the other case ρF (N) is between p and q. In both cases we obtain the time-global and unique existence of solutions for small data and their asymptotic behaviors. These observation will be applied to the corresponding system of the damped wave equations in low dimensional space.

    Original languageEnglish
    Pages (from-to)331-348
    Number of pages18
    JournalOsaka Journal of Mathematics
    Volume49
    Issue number2
    Publication statusPublished - 2012 Jun

    Fingerprint

    Semilinear Heat Equation
    Asymptotic Behavior of Solutions
    Damped
    Exponent
    Damped Wave Equation
    Heat Equation
    Existence of Solutions
    Cauchy Problem
    Asymptotic Behavior

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system. / Nishihara, Kenji.

    In: Osaka Journal of Mathematics, Vol. 49, No. 2, 06.2012, p. 331-348.

    Research output: Contribution to journalArticle

    @article{043fb88374ed48fcab746d6a4bb93953,
    title = "Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system",
    abstract = "Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is p= with p, q ≥ 1, pq > 1. When p, q satisfy max ((p+1)/(pq - 1), (q + 1)/(pq -1)) < N/2, the exponents p, q are supercritical. In this paper we assort the supercritical exponent case to two cases. In one case both p and q are bigger than the Fujita exponent ρF (N) = 1+2/N, while in the other case ρF (N) is between p and q. In both cases we obtain the time-global and unique existence of solutions for small data and their asymptotic behaviors. These observation will be applied to the corresponding system of the damped wave equations in low dimensional space.",
    author = "Kenji Nishihara",
    year = "2012",
    month = "6",
    language = "English",
    volume = "49",
    pages = "331--348",
    journal = "Osaka Journal of Mathematics",
    issn = "0030-6126",
    publisher = "Osaka University",
    number = "2",

    }

    TY - JOUR

    T1 - Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system

    AU - Nishihara, Kenji

    PY - 2012/6

    Y1 - 2012/6

    N2 - Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is p= with p, q ≥ 1, pq > 1. When p, q satisfy max ((p+1)/(pq - 1), (q + 1)/(pq -1)) < N/2, the exponents p, q are supercritical. In this paper we assort the supercritical exponent case to two cases. In one case both p and q are bigger than the Fujita exponent ρF (N) = 1+2/N, while in the other case ρF (N) is between p and q. In both cases we obtain the time-global and unique existence of solutions for small data and their asymptotic behaviors. These observation will be applied to the corresponding system of the damped wave equations in low dimensional space.

    AB - Consider the Cauchy problem for a system of weakly coupled heat equations, whose typical one is p= with p, q ≥ 1, pq > 1. When p, q satisfy max ((p+1)/(pq - 1), (q + 1)/(pq -1)) < N/2, the exponents p, q are supercritical. In this paper we assort the supercritical exponent case to two cases. In one case both p and q are bigger than the Fujita exponent ρF (N) = 1+2/N, while in the other case ρF (N) is between p and q. In both cases we obtain the time-global and unique existence of solutions for small data and their asymptotic behaviors. These observation will be applied to the corresponding system of the damped wave equations in low dimensional space.

    UR - http://www.scopus.com/inward/record.url?scp=84863482066&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84863482066&partnerID=8YFLogxK

    M3 - Article

    VL - 49

    SP - 331

    EP - 348

    JO - Osaka Journal of Mathematics

    JF - Osaka Journal of Mathematics

    SN - 0030-6126

    IS - 2

    ER -