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.