The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension

Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The critical constant µ (see (1.1)) of time-decaying damping in the scale-invariant case is recently conjectured. It also has been expected that the lifespan estimate is the same as for the associated semilinear heat equations if the constant is in the “heat-like” domain. In this paper, we point out that this is not true if the total integral of the sum of initial position and speed vanishes. In such a case, we have a new type of the lifespan estimates which is closely related to the non-damped case in shifted space dimensions.

Original languageEnglish
Pages (from-to)659-678
Number of pages20
JournalDifferential and Integral Equations
Volume32
Issue number11-12
Publication statusPublished - 2019

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension'. Together they form a unique fingerprint.

Cite this