We consider the Cauchy problem for the damped wave equation with semilinear absorbing term
utt - Δu + b(t,x)ut = -|u|ρ-1u, (t,x)∈(R+,RN).
When b(t,x)=1, it is expected that the solution has the diffusion phenomena as time tends to infinity, that is, the solution behaves samely as that for the corresponding semilinear diffusive equation as t→∞. Therefore, dependent on supercritical, critical or subcritical exponent ρ of the semilinear term, the behavior differs with each other. In the talk we will show the decay rates of solutions or the diffusion phenomena in some cases even for time or space dependent coefficient b(t,x) with suitable condition. For those proofs we employ the L2-energy method with suitable weight. Note that, since our equation is hyperbolic, we cannot apply the strong tools in the parabolic problem like the maximum principle, the smoothing effect etc.