Critical exponent for the Cauchy problem to the weakly coupled damped wave system

Kenji Nishihara, Yuta Wakasugi

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    In this paper, we consider a system of weakly coupled semilinear damped wave equations. We determine the critical exponent for any space dimensions. Our proof of the global existence of solutions for supercritical nonlinearities is based on a weighted energy method, whose multiplier is appropriately modified in the case where one of the exponent of the nonlinear term is less than the so called Fujita's critical exponent. We also give estimates of the lifespan of solutions from above for subcritical nonlinearities.

    Original languageEnglish
    Pages (from-to)249-259
    Number of pages11
    JournalNonlinear Analysis, Theory, Methods and Applications
    Volume108
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Wave equations
    Damped
    Critical Exponents
    Cauchy Problem
    Nonlinearity
    Damped Wave Equation
    Semilinear Wave Equation
    Life Span
    Energy Method
    Global Existence
    Multiplier
    Existence of Solutions
    Exponent
    Term
    Estimate

    Keywords

    • Critical exponent
    • Damped wave equation
    • Global existence
    • Lifespan
    • Weakly coupled system

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    Critical exponent for the Cauchy problem to the weakly coupled damped wave system. / Nishihara, Kenji; Wakasugi, Yuta.

    In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 108, 2014, p. 249-259.

    Research output: Contribution to journalArticle

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