On a Nonlinear Wave Equation Associated with Dirichlet Conditions : Solvability and Asymptotic Expansion of Solutions in Many Small Parameters

الملخص EN

A Dirichlet problem for a nonlinear wave equation is investigated.

Under suitable assumptions, we prove the solvability and the uniqueness of a weak solution of the above problem.

On the other hand, a high-order asymptotic expansion of a weak solution in many small parameters is studied.

Our approach is based on the Faedo-Galerkin method, the compact imbedding theorems, and the Taylor expansion of a function.