On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lema\^{i}tre-Robertson-Walker spacetime

TL;DR

This paper investigates the lifespan of solutions to a nonlinear wave equation in Friedmann-Lemaître-Robertson-Walker spacetime, providing upper bounds for blow-up solutions in subcritical and critical cases.

Contribution

It introduces upper bounds for the lifespan of blow-up solutions in heatlike nonlinear wave equations within a cosmological spacetime context.

Findings

Upper bounds for blow-up solution lifespan established

Distinction between subcritical and critical cases clarified

Lifespan estimates influenced by the Fujita exponent

Abstract

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetimes. We treat the so-called heatlike case where the critical exponent is affected by the Fujita exponent. We show upper bounds of the lifespan of blow-up solutions by distinguishing subcritical and critical cases.