Nonlinear dissipative wave equations with space–time dependent potential

We study the long time behavior of solutions for damped wave equations with absorption. These equations are generally accepted as models of wave propagation in heterogeneous media with space–time dependent friction a(t,x)uta(t,x)ut and nonlinear absorption |u|p−1u|u|p−1u (Ikawa (2000) [17]). We consider 1