Blow-up for Strauss type wave equation with damping and potential

Wei Dai, Hideo Kubo, Motohiro Sobajima

Research output: Contribution to journalArticle

Abstract

We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.

Original languageEnglish
Article number103195
JournalNonlinear Analysis: Real World Applications
Volume57
DOIs
Publication statusPublished - Feb 2021

Keywords

  • Blow-up
  • Critical exponent
  • Damping
  • Potential

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