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

Here we study uniform exponential stabilization of the vibrations of Kirchhoff type wave equation in a bounded domain in Rn 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.