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 L2 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.