Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime

Abstract

In this paper, we prove some blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime by using an iteration argument and we derive upper bound estimates for the lifespan. In particular, we will focus on the critical cases which require the employment of a slicing procedure in the iterative mechanism. Furthermore, in order to deal with the main critical case, we will introduce a non-autonomous and parameter-dependent Cauchy problem for a linear ODE of second-order, whose explicit solution will be determined by applying the theory of special functions.

References in corpus (2)

• Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
• Lifespan of semilinear generalized Tricomi equation with Strauss type exponent

Cited by in corpus (5)

• 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
• 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