Stability of Timoshenko systems with thermal coupling on the bending moment

The Timoshenko system is a distinguished coupled pair of differential equations arising in mathematical elasticity. In the case of constant coefficients, if a damping is added in only one of its equations, it is well-known that exponential stability holds if and only if the wave speeds of both equations are equal. In the present paper we study both non-homogeneous and homogeneous thermoelastic problems where the model's coefficients are non-constant and constants, respectively. Our main stability results are proved by means of a unified approach that combines local estimates of the resolvent equation in the semigroup framework with a recent control-observability analysis for static systems. Therefore, our results complement all those on the linear case provided in [22], by extending the methodology employed in [4] to the case of Timoshenko systems with thermal coupling on the bending moment.