Global existence for semilinear wave equations with the critical blow-up term in high dimensions

Hiroyuki Takamura, Kyouhei Wakasa

Research output: Contribution to journalArticlepeer-review

Abstract

We are interested in almost global existence cases in the general theory for nonlinear wave equations, which are caused by critical exponents of nonlinear terms. Such situations can be found in only three cases in the theory, cubic terms in two space dimensions, quadratic terms in three space dimensions and quadratic terms including a square of unknown functions itself in four space dimensions. Except for the last case, criteria to classify nonlinear terms into the almost global, or global existence case, are well-studied and known to be so-called null condition and non-positive condition.Our motivation of this work is to find such a kind of the criterion in four space dimensions. In our previous paper, an example of the non-single term for the almost global existence case is introduced. In this paper, we show an example of the global existence case. These two examples have nonlinear integral terms which are closely related to derivative loss due to high dimensions. But it may help us to describe the final form of the criterion.

Original languageEnglish
Pages (from-to)1046-1067
Number of pages22
JournalJournal of Differential Equations
Volume261
Issue number2
DOIs
Publication statusPublished - 2016 Jul 15

Keywords

  • Critical exponent
  • High dimensions
  • Lifespan
  • Semilinear wave equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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