Exponential Stability of a System of Linear Timoshenko Type with Boundary Controls

In the present paper we consider the stabilization problem of porous elastic solids in real world. The kinetic behavior of porous solids is governed by equations of linear Timoshenko type which is generally asymptotically stable but not exponentially stable. In this paper we act boundary velocity feedback controls on the system with both ends free. Then we discuss its well-posed-ness and obtain the exponential stability of the closed loop system by use of the Riesz basis property and spectral distribution.