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

Kazumasa Fujiwara, Tohru Ozawa

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

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
Volume9
Issue number53-56
DOIs
Publication statusPublished - 2015

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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