Exponential energy decay estimates for the solutions of n-dimensional Kirchhoff type wave equation

Abstract

Here we study uniform exponential stabilization of the vibrations of Kirchhoff type wave equation in a bounded domain in R n with a smooth boundary, under mixed boundary conditions. To stabilize the system, we incorporate separately, the passive viscous damping and the internal material damping of Kelvin–Voigt type in the model. Explicit forms of exponential energy decay rates are obtained by a direct method, for the solution of such boundary value problems.