Asymptotic behaviors of solutions for viscoelastic wave equation with space–time dependent damping term

In this paper, we consider a viscoelastic wave equation with an absorbing term and space–time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L 2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term.