The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions

Takuto Imai, Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we study the initial value problem for semilinear wave equations with the time-dependent and scale-invariant damping in two dimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa in 2019, we obtain the lifespan estimates of the solution for a special constant in the damping term, which are classified by total integral of the sum of the initial position and speed. The key fact is that, only in two space dimensions, such a special constant in the damping term is a threshold between “wave-like” domain and “heat-like” domain. As a result, we obtain a new type of estimate especially for the critical exponent.

Original languageEnglish
Pages (from-to)8387-8424
Number of pages38
JournalJournal of Differential Equations
Volume269
Issue number10
DOIs
Publication statusPublished - 2020 Nov 5

Keywords

  • Lifespan
  • Scale-invariant damping
  • Semilinear wave equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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