LINEAR APPROXIMATION AND ASYMPTOTIC EXPANSION ASSOCIATED TO THE ROBIN-DIRICHLET PROBLEM FOR A NONLINEAR WAVE EQUATION WITH THE SOURCE TERM CONTAINING AN UNKNOWN BOUNDARY VALUE

Abstract

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equa- tion with the source term containing an unknown boundary value. Using the Faedo-Galerkin method and the linearization method for nonlinear term, the existence and uniqueness of a weak solution are proved. An asymptotic expansion of high order in a small parameter of a weak solution is also discussed.