Abstract
In this article, we use the Euler–Bernoulli model to study the vibrations of a beam composed of two components, one consisting of a thermoelastic material and the other of a simply elastic material that does not produce dissipation. Our main result is that the semigroup associated with this model is differentiable. In particular, our proof implies the following properties of the semigroup (1) It is of Gevrey class 12. (2) It is exponentially stable. (3) It possesses the property of linear stability and has a regularizing effect on the initial data.
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Acknowledgements
The authors would like to thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), process number: 88882 33266/2019-01 and CNPq Project 310249/2018-0, for the financial support.
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Sozzo, B.T.S., Rivera, J.E.M. Gevrey class for locally thermoelastic beam equations. Z. Angew. Math. Phys. 73, 153 (2022). https://doi.org/10.1007/s00033-022-01800-1
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DOI: https://doi.org/10.1007/s00033-022-01800-1