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

Nguyen Huu Nhan, Nguyen Thanh Than, Le Thi PhuongNgoc, Nguyen Thanh Long

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.


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ISSN: 1229-1595 (Print), 2466-0973 (Online)