Remarks on global solutions to the cauchy problem for semirelativistic equations with power type nonlinearity

Kazumasa Fujiwara, Tohru Ozawa

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    4 Citations (Scopus)


    Existence and nonexistence results on global solutions to the Cauchy problem for semirelativistic equations are shown by a simple compact- ness argument and a test function method, respectively. To obtain the nonexistence of global solutions, semirelativistic equations are trans- formed into a new equation without nonlocal operators in linear part but with a time derivative in nonlinear part, which is shown to be under control of special choice of test functions.

    Original languageEnglish
    Pages (from-to)2599-2610
    Number of pages12
    JournalInternational Journal of Mathematical Analysis
    Issue number53-56
    Publication statusPublished - 2015



    • Compactness argument
    • Nonexistence of weak solutions
    • Semirelativistic equation
    • Test function method

    ASJC Scopus subject areas

    • Mathematics(all)

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