Asymptotic behaviors of solutions for time dependent damped wave equations

In this paper, we consider the Cauchy problem for the wave equation with time dependent damping b(t)ut and absorbed semilinear term |u|ρ−1u. Here, b(t)=b0(1+t)−β with −1<β<1 and b0>0. Using the weighted energy method, we obtain the L1 and L2 decay rates of the solution, which coincide to those for self-similar solutions to the corresponding parabolic equation when .