Existence and general decay estimates of the Dirichlet problem for a nonlinear Kirchhoff wave equation in an annular with viscoelastic term

This paper is devoted to the study of a Kirchhoff wave equation with viscoelastic term in an annular associated homogeneous Dirichlet conditions. At first, by applying Faedo-Galerkin, we prove existence and uniqueness solution problem considered. Next, constructing Lyapunov functional, establish sufficient condition such that any global weak general decay as t → +∞.