Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime

Abstract

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions.The blow-up condition is the same as in the accelerated expanding Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We also show the same results for the space derivative nonlinear term.

arXiv comment15 pages

References in corpus (4)

• Friedmann's Equations in All Dimensions and Chebyshev's Theorem
• A note on the lifespan of solutions to the semilinear damped wave equation
• The Cauchy problem for the nonlinear damped wave equation with slowly decaying data
• Finite lifespan of solutions of the semilinear wave equation in the Einstein-de Sitter spacetime

Cited by in corpus (2)

• A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes
• On a semilinear wave equation in anti-de Sitter spacetime: the critical case