Non-exponential stability to a Timoshenko system with heat conduction and Kelvin–Voigt damping

We consider a Timoshenko system with partially Kelvin–Voigt damping, and with Cattaneo/Fourier type heat conduction. When the Timoshenko system with only heat conduction or only partially Kelvin–Voigt damping, some authors showed the non-exponential stability. In this paper, we add the Kelvin–Voigt...

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Bibliographic Details
Published in:Applied mathematics letters 2023-06, Vol.140, p.108592, Article 108592
Main Authors: Cui, Jianan, Chai, Shugen
Format: Article
Language:English
Subjects:
Heat conduction
Kelvin–Voigt damping
Non-exponential stability
Optimal decay
Timoshenko system
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Summary:We consider a Timoshenko system with partially Kelvin–Voigt damping, and with Cattaneo/Fourier type heat conduction. When the Timoshenko system with only heat conduction or only partially Kelvin–Voigt damping, some authors showed the non-exponential stability. In this paper, we add the Kelvin–Voigt damping in the thermoelastic Timoshenko system, and prove that the system is also not exponentially stable in cases of Fourier and Cattaneo type heat conduction, whether the wave speeds are equal or not. Additionally, we prove the semigroup decays with the optimal rate t−12.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2023.108592