On a thermoelastic Timoshenko system without the second spectrum: Existence and stability

Abstract

In this work we study the well-posedness and the asymptotic stability of a linear thermoelastic Timoshenko system free of second spectrum, where the heat conduction is given by Cattaneo’s law. We give a detailed proof of the well-posedness, using the semigroup theory. Then, we prove that the system is exponentially stable irrespective of the coefficients. We also illustrate our theoretical results by performing some numerical tests.

Keywords:

• Cattaneo’s law
• exponential decay
• second spectrum
• Timoshenko system

Acknowledgments

The authors thank both reviewers for their valuable comments which improved the quality of our paper, and University of Adrar, University of Sharjah, and University of Lille for their support.

Data availability statement

No data are involved in this research.

Disclosure statement

The authors have no conflict of interest.

Additional information

Funding

A. Keddi is partially supported by the DGRSDT of Algeria and S. A. Messaoudi is sponsored by KFUPM project-INCB2311.