Generalized approach for stability numbers of shear-damped Bresse systems with Cattaneo couplings

Abstract

In this paper, by means of two general lemmas applicable to a wide variety of cases, we present a general formulation for the stability numbers associated with the thermoelastic Bresse system with heat flux given by Cattaneo's law and use it to show exponential stability of shear-damped versions of this system.

Keywords:

• Curved beams
• Cattaneo's law
• exponential stability
• linear thermoelasticity
• shear damping

2020 Mathematics Subject Classifications:

• 35B40
• 35E15
• 35Q74
• 74B05
• 74F05

Acknowledgments

The author is grateful for the comments of the anonymous reviewers, which helped to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).