Abstract

We study the initial-boundary value problem for a nonlinear wave equation given by (1) where ; , ; , are given constants and , , , , are given functions. In this paper, we consider three main parts. In Part 1 we prove a theorem of existence and uniqueness of a weak solution of problem (1). The proof is based on a Faedo–Galerkin method associated with a priori estimates, weak convergence and compactness techniques. Part 2 is devoted to the study of the asymptotic behavior of the solution as . Finally, in Part 3 we obtain an asymptotic expansion of the solution of the problem (1) up to order in three small parameters , , .