Stability of Timoshenko systems with thermal coupling on the bending moment

• Published in: Mathematische Nachrichten 2019-12, Vol.292 (12), p.2537-2555
• Main Authors: Cardozo, C. L., Jorge Silva, M. A., Ma, T. F., Muñoz Rivera, J. E.
• Format: Article
• Language: English
• Subjects: 35B35; 35B40; 35M33; 74D05; 74K10; Bending moments; Damping; Differential equations; Elasticity; exponential stability; polynomial decay; Stability; Thermal coupling; thermoelasticity; Timoshenko system
• ISSN: 0025-584X; 1522-2616
• DOI: 10.1002/mana.201800546

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.