Existence of global smooth solution to the initial boundary value problem for p-system with damping

This paper is concerned with the initial boundary value problem for the p$p$-system with damping. We prove the existence of the global smooth solution under the assumption that only the C⁰$C^0$-norm of the derivative of the initial data is sufficiently small, while the C⁰$C^0$-norm of the initial data is not necessarily small. The proof is based on several key a priori estimates, the maximum principle and the characteristic method.