Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term

TL;DR

This paper investigates blow-up phenomena and lifespan estimates for semilinear wave equations with scattering damping and negative mass term, revealing that the blow-up behavior matches that of simpler related problems.

Contribution

It introduces a novel comparison argument and multiplier technique to analyze blow-up in wave equations with combined damping and negative mass effects.

Findings

Blow-up occurs for subcritical power in the studied equations.

Lifespan estimates match those of related simpler problems.

The method applies to equations with scattering damping and negative mass term.

Abstract

In this paper we establish blow-up results and lifespan estimates for semilinear wave equations with scattering damping and negative mass term for subcritical power, which is the same as that of the corresponding problem without mass term, and also the same as that of the corresponding problem without both damping and mass term. For this purpose, we have to use the comparison argument twice, due to the damping and mass term, in additional to a key multiplier. Finally, we get the desired results by an iteration argument.