L_p-convergence rate to nonlinear diffusion waves for p-system with damping

In this paper, we study the p-system with frictional damping and show that the solutions time-asymptotically tend to the nonlinear diffusion waves governed by the classical Darcy's law. By introducing an approximate Green function, we obtain the optimal L_p, 2≤p≤+∞, convergence rate of the solution, which is a perturbation of the nonlinear diffusion wave, to the hyperbolic system.