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

By Le Huu Ky Son, Nguyen Le Thi
DOI: 10.37550/tdmu.EJS/2023.05.417

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 → +∞.