Exponential stability of viscoelastic structure with second sound

Authors

Ganesh C. Gorain Department of Mathematics, J. K. College, Purulia 723101, West Bengal, India https://orcid.org/0000-0002-5326-3635
Carlos Raposo PhD Program in Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil Corresponding Author https://orcid.org/0000-0001-8014-7499
Octavio Vera Department of Mathematics, Universidad de Tarapac´a, Arica, Chile https://orcid.org/0000-0001-7304-0976
Srikanta Ram Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, India https://orcid.org/0009-0005-9089-5286

DOI:

https://doi.org/10.61383/ejam.20242250

Keywords:

Viscoelastic structure, Cattaneo’s law, existence of solution, exponential decay

Abstract

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.

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Published

2024 Jun 10

Issue

Vol. 2 No. 2 (2024)

Section

Research Article

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This work is licensed under a Creative Commons Attribution 4.0 International License.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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“Exponential stability of viscoelastic structure with second sound”, Electron. J. Appl. Math., vol. 2, no. 2, pp. 10–21, Jun. 2024, doi: 10.61383/ejam.20242250.

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