About the stability to Timoshenko system with pointwise dissipation

Jaime E. Muñoz Rivera; Maria Grazia Naso

doi:10.3934/dcdss.2022078

Article Contents

2022, Volume 15, Issue 8: 2289-2303. Doi: 10.3934/dcdss.2022078

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About the stability to Timoshenko system with pointwise dissipation

Jaime E. Muñoz Rivera^1, , and
Maria Grazia Naso^2,

1.
National Laboratory for Scientific Computation, Rua Getulio Vargas 333, Petrópolis, RJ, Brazil, DMAT - Universidad del Bío-Bío, Avenida Collao 1202, Casilla 5 - Concepción, Chile, IM - UFRJ, Cidade Universitária, Rio de Janeiro, Brazil
2.
DICATAM, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy

^* Corresponding author
^* Corresponding author

In honor of Maurizio Grasselli's 60th Birthday

Received: November 30, 2021

Published: August 2022

The first author is supported by Brazilian - CNPq grant 310249/2018-0 while the second one is partially supported by the Gruppo Nazionale per la Fisica Matematica of the Istituto Nazionale di Alta Matematica

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Abstract

In this paper we study the Timoshenko model over the interval $ (0, \ell) $ with pointwise dissipation at $ \xi\in (0, \ell) $. We prove that this dissipation produces exponential stability when $ \xi\in \mathbb{Q}\ell $ and $ \xi\ne \frac{n}{2m+1}\ell $, where $ n, m\in \mathbb{N} $ and $ n $, and $ 2m+1 $ are co-prime.

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Mathematics Subject Classification: Primary: 35B35, 35Q74; Secondary: 74H40, 74K10, 93D15.

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References

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