Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application

Kenji Nishihara

    Research output: Contribution to journalArticle

    153 Citations (Scopus)

    Abstract

    It has been asserted that the damped wave equation has the diffusive structure as t → ∞. In this paper we consider the Cauchy problem in 3-dimensional space for the linear damped wave equation and the corresponding parabolic equation, and obtain the Lp - Lq estimates of the difference of each solution, which represent the assertion precisely. Explicit formulas of the solutions are analyzed for the proof. The second aim is to apply the Lp - Lq estimates to the semilinear damped wave equation with power nonlinearity. If the power is larger than the Fujita exponent, then the time global existence of small weak solution is proved and its optimal decay order is obtained.

    Original languageEnglish
    Pages (from-to)631-649
    Number of pages19
    JournalMathematische Zeitschrift
    Volume244
    Issue number3
    Publication statusPublished - 2003 Jul

    Fingerprint

    Lp Estimates
    Damped Wave Equation
    Semilinear Wave Equation
    Assertion
    Global Existence
    Parabolic Equation
    Weak Solution
    Explicit Formula
    Cauchy Problem
    Exponent
    Nonlinearity
    Decay

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application. / Nishihara, Kenji.

    In: Mathematische Zeitschrift, Vol. 244, No. 3, 07.2003, p. 631-649.

    Research output: Contribution to journalArticle

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