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

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.

arXiv comment40 pages. Introduction and References are updated

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Cited by in corpus (4)

• Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma
• The semilinear Euler-Poisson-Darboux equation: a case of wave with critical dissipation
• Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
• A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term