On the nonexistence of global solutions for critical semilinear wave equations with damping in the scattering case

Abstract

We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in Rn, where n≥2. It is expected that the critical exponent will be Strauss’ number p0(n), which is also the one for semilinear wave equations without damping terms.Lai and Takamura (2018) have obtained the blow-up part, together with the upper bound of lifespan, in the sub-critical case p<p0(n). In this paper, we extend their results to the critical case p=p0(n). The proof is based on Wakasa and Yordanov (0000), which concerns the blow-up and upper bound of lifespan for critical semilinear wave equations with variable coefficients.