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

Abstract

This paper is concerned with the initial boundary-value problem for the p-system with nonlinear damping. We prove the existence of a global smooth solution under the assumption that only the C0-norm of the derivative of the initial data is sufficiently small, while the C0-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.