Existence of global smooth solution to initial boundary value problem for a viscoelastic model with relaxation

This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C-0-norm of the initial data is small, without smallness hypothesis for the C-1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the "maximum principle" of first-order quasilinear hyperbolic system.