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

Kenji Nishihara

    研究成果: Article

    10 引用 (Scopus)

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    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.

    元の言語English
    ページ(範囲)331-348
    ページ数18
    ジャーナルOsaka Journal of Mathematics
    49
    発行部数2
    出版物ステータスPublished - 2012 6

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    ASJC Scopus subject areas

    • Mathematics(all)

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