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Stability of a Timoshenko System with Localized Kelvin–Voigt Dissipation

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Abstract

We consider the Timoshenko beam with localized Kelvin–Voigt dissipation distributed over two components: one of them with constitutive law of the type \(C^1\), and the other with discontinuous law. The third component is simply elastic, where the viscosity is not effective. Our main result is that the decay depends on the position of the components. We will show that the system is exponentially stable if and only if the component with discontinuous constitutive law is not in the center of the beam. When the discontinuous component is in the middle, the solution decays polynomially.

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Acknowledgements

The authors would like to express their deepest gratitude to the anonymous referees for their comments and suggestions that have contributed greatly to the improvement of this article. G. Aguilera Contreras is supported by ANID-PFCHA grant for doctoral studies, academic year 2017, no. 21171212. J. Muñoz Rivera is supported by CNPq-Brazil Project 310249/2018-0.

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Authors and Affiliations

  1. Department of Mathematics, University of Bio-Bio, Concepción, Chile

    Gabriel Aguilera Contreras & Jaime E. Muñoz Rivera

  2. LNCC, Petrópolis, RJ, Brazil

    Jaime E. Muñoz Rivera

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  1. Gabriel Aguilera Contreras
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  2. Jaime E. Muñoz Rivera
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Correspondence to Gabriel Aguilera Contreras.

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Aguilera Contreras, G., Muñoz Rivera, J.E. Stability of a Timoshenko System with Localized Kelvin–Voigt Dissipation. Appl Math Optim 84, 3547–3563 (2021). https://doi.org/10.1007/s00245-021-09758-8

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  • DOI: https://doi.org/10.1007/s00245-021-09758-8

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