On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime

Abstract

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lemaître-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.

16 pages

References in corpus (3)

• Friedmann's Equations in All Dimensions and Chebyshev's Theorem
• Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
• Life-Span of Semilinear Wave Equations with Scale-invariant Damping: Critical Strauss Exponent Case

Cited by in corpus (6)

• A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime
• On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity
• Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type
• On a semilinear wave equation in anti-de Sitter spacetime: the critical case
• On Glassey's conjecture for semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime
• Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime