Exponential Stability of Viscoelastic Structure with Second Sound

This manuscript deals with a thermo-viscoelastic system describing the vibrations of a flexible structure. We study this structure's stabilization problem when subjected to Kelvin-Voigt damping and the second sound. Cattaneo-Vernotte's law governs the thermal effect, eliminating the physic...

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Bibliographic Details
Published inElectronic Journal of Applied Mathematics Vol. 2; no. 2; pp. 10 - 21
Main Authors C. Gorain, Ganesh, Carlos, Vera, Octavio, Ram, Srikanta
Format Journal Article
LanguageEnglish
Published 10.06.2024
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Summary:This manuscript deals with a thermo-viscoelastic system describing the vibrations of a flexible structure. We study this structure's stabilization problem when subjected to Kelvin-Voigt damping and the second sound. Cattaneo-Vernotte's law governs the thermal effect, eliminating the physical paradox of equal speed of waves in the classical thermoelastic theory. Semigroup theory proves the solution's existence and uniqueness. Exponential stability is proved by the energy method.
ISSN:2980-2474
2980-2474
DOI:10.61383/ejam.20242250