Global existence for time-dependent damped wave equations with nonlinear memory

In this article, we consider the Cauchy problem for a semi-linear wave equation with time-dependent damping and memory nonlinearity. Conditions for global existence are presented in the energy space H1(Rn)×L2(Rn){H}^{1}\left({{\mathbb{R}}}^{n})\times {L}^{2}\left({{\mathbb{R}}}^{n}), n≥1n\ge 1.