Energy decay to Timoshenko's system with thermoelasticity of type III

We consider the thermoelastic beam system when the oscillations are defined by the Timoshenko's model and the heat conduction is given by Green and Naghdi theories. Our main result is that the corresponding semigroup is exponentially stable if and only if the wave speeds associated to the hyperbolic part of the system are equal. In the case of lack of exponential stability we show that the solution decays polynomially and we prove that the rate of decay is optimal.

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