A mixed Dirichlet–Robin problem for a nonlinear Kirchhoff–Carrier wave equation

In this paper, a mixed Dirichlet–Robin problem for a nonlinear Kirchhoff–Carrier wave equation is studied. Using the Faedo–Galerkin method and the linearization method for nonlinear terms, we prove the existence and uniqueness of a weak solution of the above problem. An asymptotic expansion of high order in many small parameters of solutions is also discussed.