Frequency domain approach for the stabilization of Timoshenko-type system of thermoelasticity of type III (Q2928673)

In this paper, the authors study the energy decay rate for the one-dimensional linear thermoelastic system of Timoshenko type. This system models the transverse vibration of a thick beam, taking into account the heat conduction given by Green and Naghdi's theory where the dissipation is given by the heat conduction of type III. First, the authors establish a polynomial energy decay in the case of unequal speeds. Second, when the wave speeds are equal, an exponential type decay is obtained. The proof is based on the frequency domain approach.