Effects of Kelvin–Voigt Damping on the Stability of (Thermo)Elastic Timoshenko System with Second Sound

In this paper, we investigate the stabilization of Timoshenko systems with or without Kelvin–Voigt damping, in the presence of second sound. We have drawn conclusions that provide new insights into the effect of local Kelvin–Voigt damping. Our primary conclusion is that the exponential stability of...

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Bibliographic Details
Published in:Applied mathematics & optimization 2024-02, Vol.89 (1), p.23, Article 23
Main Authors: Cui, Jianan, Chai, Shugen
Format: Article
Language:English
Subjects:
Applied mathematics
Calculus of Variations and Optimal Control
Optimization
Control
Damping
Heat
Investigations
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Noise control
Numerical and Computational Physics
Optimization
Simulation
Stability
Systems Theory
Theoretical
Viscoelasticity
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Summary:In this paper, we investigate the stabilization of Timoshenko systems with or without Kelvin–Voigt damping, in the presence of second sound. We have drawn conclusions that provide new insights into the effect of local Kelvin–Voigt damping. Our primary conclusion is that the exponential stability of the system achieved through local thermal damping will be destroyed by the local Kelvin–Voigt damping with a discontinuous coefficient at the interface. In particular, when local dissipation solely originates from the second sound, the system exhibits exponential stability. However, when Kelvin–Voigt damping is introduced into the local thermoelastic component, the system, surprisingly, loses its exponential stability. In this case, the corresponding solution decays polynomially with the rate t - 2 .
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-023-10098-y