Finite time blow-up for damped wave equations with space–time dependent potential and nonlinear memory

In this paper, we consider the Cauchy problem in Rn, n≥ 1 , for semilinear damped wave equations with space–time dependent potential and nonlinear memory. A blow-up result under some positive data in any dimensional space is obtained. Moreover, the local existence in the energy space is also studied. © 2018, Springer Nature Switzerland AG.