Improved Kato's lemma on ordinary differential inequality and its application to semilinear wave equations

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18 Citations (Scopus)

Abstract

Abstract We are interested in the upper bound of the lifespan of solutions of semilinear wave equations. For the sub-critical case in high dimensions, it has been believed that the basic tools of its analysis are Kato's lemma on ordinary differential inequalities and the rescaling argument in the functional method. But there is a small lack of delicate analysis and no published paper about this. Here we give a simple alternative proof by means of improved Kato's lemma without any rescaling argument.

Original languageEnglish
Article number10539
Pages (from-to)227-240
Number of pages14
JournalNonlinear Analysis, Theory, Methods and Applications
Volume125
DOIs
Publication statusPublished - 2015 Jun 13
Externally publishedYes

Keywords

  • Lifespan
  • Ordinary differential inequality
  • Semilinear wave equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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