In this talk, we are concerned with the asymptotic behavior of solutions to the system of Euler equationswith time-depending damping, in particular, include theconstant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Our results include the cases of Cauchy problem and initial boundary value problem.The proof is based on the classical energy method. This is a joint work with Haibo Cui and Haiyan Yin.