Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass

2019/04/21 by Ikeda, Masahiro, Tu, Ziheng, Wakasa, Kyouhei
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.09574

Abstract

In the present paper, we study small data blow-up of the semi-linear wave equation with a scattering dissipation term and a time-dependent mass term from the aspect of wave-like behavior. The Strauss type critical exponent is determined and blow-up results are obtained to both sub-critical and critical cases with corresponding upper bound lifespan estimates. For the sub-critical case, our argument does not rely on the sign condition of dissipation and mass, which gives the extension of the result in \citeLai-Sch-Taka18. Moreover, we show the blow-up result for the critical case which is a new result.

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