Solvability, continuous dependence and asymptotic expansion of solutions in a small parameter of Dirichlet problem for a nonlinear Kirchhoff wave equation

We study the existence, uniqueness, continuous dependence, and asymptotic expansion of solutions of the Dirichlet problem for a nonlinear Kirchhoff wave equation. At first, we state and prove a theorem involving the local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the nonlinear terms. Finally, an asymptotic expansion of high order in a small parameter of a weak solution is also discussed.