Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case

Ning An Lai, Hiroyuki Takamura

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

It is well-known that the critical exponent for semilinear damped wave equations is Fujita exponent when the damping is effective. Lai, Takamura and Wakasa in 2017 have obtained a blow-up result not only for super-Fujita exponent but also for the one closely related to Strauss exponent when the damping is scaling invariant and its constant is relatively small, which has been recently extended by Ikeda and Sobajima. Introducing a multiplier for the time-derivative of the spatial integral of unknown functions, we succeed in employing the techniques on the analysis for semilinear wave equations and proving a blow-up result for semilinear damped wave equations with sub-Strauss exponent when the damping is in the scattering range.

Original languageEnglish
Pages (from-to)222-237
Number of pages16
JournalNonlinear Analysis, Theory, Methods and Applications
Volume168
DOIs
Publication statusPublished - 2018 Mar
Externally publishedYes

Keywords

  • Blow-up
  • Damped wave equation
  • Lifespan
  • Semilinear

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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