Timoshenko systems with Cattaneo law and partial Kelvin–Voigt damping: well-posedness and stability

Abstract

This work considers thermoelastic Timoshenko beam systems with full and partial Kelvin–Voigt damping. The heat conduction is governed by the Cattaneo law. By applying the semi-group method, we establish the existence and uniqueness of weak global solution, then with the multiplier method, we as well prove exponential stability results. In most cases, stabilizing a Timoshenko system with Cattaneo law requires obtaining stability number or some equal wave speed propagation condition. However, interestingly in this work our stability result does not require any stability number nor equal wave speed propagation condition.

Keywords:

• Timoshenko
• thermoelasticity
• Cattaneo law
• Kelvin–Voigt
• well-posedness
• stability

2010 MSC:

• 35D30
• 35D35
• 35B35

Acknowledgements

The author appreciates the continuous support of University of Hafr Al Batin. The author is grateful to the esteemed referees for their comments which improved the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.