On a wave equation containing nonlinear integral terms: Existence and asymptotic expansion of solutions

In this paper, we consider an initial-boundary problem for a wave equation containing nonlinear integral terms. By the linear approximate method associated with the Faedo-Galerkin method, the existence and uniqueness of solutions for the proposed problem are proved. Moreover, a high-order asymptotic expansion in a small parameter of the weak solution is also discussed.

Keywords:

Wave Equation , Faedo-Galerkin method , Recurrent sequence , Asymptotic expansion , Nonlinear integral terms