Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime

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. For the case of accelerated expansion, 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. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.