Blow-up for semilinear damped wave equations with sub-Strauss and Strauss exponent in the scattering case

Ning-An Lai, Hiroyuki Takamura

Published 2017-07-30Version 1

It is well-known that the critical exponent for semilinear damped wave equations is Fujita exponent when the damping is effective. Recently, Lai, Takamura and Wakasa have obtained a blow-up result not only for the bigger one but also for the one closely related to Strauss exponent when the damping is scaling invariant and its constant is relatively small. Introducing a multiplier for the time-derivative of the spatial integral of unknown functions, we succeed in employing the technics on the analysis for semilinear wave equations and proving a blow-up result for semilinear damped wave equations with sub-Strauss and Strauss exponent when the damping is in the scattering range.