Global existence and blow-up for semilinear damped wave equations in three space dimensions

We consider initial value problem for semilinear damped wave equations in three space dimensions. We show the small data global existence for the problem without the spherically symmetric assumption and obtain the sharp lifespan of the solutions. This paper is devoted to a proof of the Takamura’s conjecture in D’Abbicco et al. (2015) on the lifespan of solutions.