Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity

TL;DR

This paper investigates the lifespan and blow-up behavior of solutions to a semilinear wave equation with scale-invariant dissipation and mass, identifying critical exponents and providing lifespan estimates for sub-critical and critical cases.

Contribution

It determines the Strauss type critical exponent for the model and establishes blow-up results with lifespan bounds, extending understanding of wave equations with scale-invariant damping and mass.

Findings

Identified the critical exponent for blow-up.

Proved blow-up results for sub-critical and critical cases.

Provided upper bound lifespan estimates.

Abstract

In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper bound for the exponent in the nonlinearity in the main theorems. Two blow-up results are obtained for the sub-critical case and for the critical case, respectively. In both cases, an upper bound lifespan estimate is given.