Finite lifespan of solutions of the semilinear wave equation in the Einstein-de Sitter spacetime

Abstract

We examine the solutions of the semilinear wave equation, and, in particular, of the ${\phi }^p$ model of quantum field theory in the curved space-time. More exactly, for $1<p<4$ we prove that solution of the massless self-interacting scalar field equation in the Einstein-de Sitter universe has finite lifespan.

Reviews in Mathematical Physics in press

Cited by in corpus (11)

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• Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
• 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
• Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime
• On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity
• Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime
• Fundamental solutions of the Dirac operator in the Friedmann-Lemaître-Robertson-Walker spacetime
• Semilinear wave equation on compact Lie groups
• 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
• Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime