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

[摘要] 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. (c) 2020 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

[发布日期] 2020-11-05

[关键词] Semilinear wave equation;Scale-invariant damping;Lifespan