Lp-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 Darcyʹs law. By introducing an approximate Green function, we obtain the optimal Lp, 2 p +∞, convergence rate of the solution, which is a perturbation of the nonlinear diffusion wave, to the hyperbolic system