Blow up of solutions of semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann–Lemaître–Robertson–Walker spacetimes. For the case of decelerating expansion, we show upper bounds of the lifespan of blow-up solutions by distinguishing subcritical and critical cases. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.