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

Abstract

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