Best asymptotic profile for linear damped p-system with boundary effect

This paper is devoted to the study of the 2×2 linear damped p-system with boundary effect. By a heuristic analysis, we realize that the best asymptotic profile for the original solution is the parabolic solution of the IBVP for the corresponding porous media equation with a specified initial data. In particular, we further show the convergence rates of the original solution to its best asymptotic profile, which are much better than the existing rates obtained in the previous works. The approach adopted in the paper is the elementary weighted energy method with Green function method together.