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

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)8387-8424
ページ数38
ジャーナルJournal of Differential Equations
269
10
DOI
出版ステータスPublished - 2020 11 5

ASJC Scopus subject areas

  • 分析
  • 応用数学

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