EXPONENTIAL DECAY OF WEAK SOLUTION OF THE DIRICHLET PROBLEM FOR THE NONLINEAR KIRCHHOFF IN AN ANNULAR MEMBRANE

Abstract

This paper is devoted to the study of the nonlinear Kirchhoff wave equation in an annual associated with homogeneous Dirichlet boundary conditions. At first, by applying the Faedo[1]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 → +¥