Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-Carrier type with Balakrishnan-Taylor damping

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on initial data, local existence and uniqueness weak solution are proved. Next, an asymptotic expansion solutions in small parameter high order is established. The used main tools linearization method terms together Faedo-Galerkin method, key lemmas high-order polynomials Taylor multi-variable functions.