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

Abstract

Abstract 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 H 1 ( R n ) × L 2 ( R n ) {H}^{1}\left({{\mathbb{R}}}^{n})\times {L}^{2}\left({{\mathbb{R}}}^{n}) , n ≥ 1 n\ge 1 .