Pointwise estimates and Lp convergence rates to diffusion waves for p-system with damping

By introducing a new approximate Green function, we obtain the pointwise estimates on the solutions of Euler equations with linear frictional damping, from which we can deduce the optimal Lp (1 p +∞) convergence rates to the nonlinear diffusion waves. The pointwise estimates and Lp (1 p<2) convergence rates given in this paper are new.