Abstract
In this paper we investigate two examples of thermoelastic plates free of the paradox of instantaneous propagation of thermal or mechanical waves when only one of them is dissipative and the other is conservative. To be precise we consider a Moore–Gibson–Thompson plate with type II heat conduction and a conservative elastic plate with Moore–Gibson–Thompson heat conduction. In both cases we prove the well-posedness. In the first case we also show the exponential decay of the solutions, but in the second we obtain the lack of the exponential decay and the optimality of the polynomial decay with rate of decay of type \(O(t^{-1})\) for the associated semigroup.
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Acknowledgements
The authors want to thank the anonymous referee for his/her useful comments, which helped us to improve the paper.
Funding
This paper is part of the project PID2019-105118GB-I00, funded by the Spanish Ministry of Science, Innovation and Universities and FEDER “A way to make Europe”. Hugo D. Fernández Sare is supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq - Brazil grant 406621/2021-7 and Fundação de Amparo à Pesquisa do Estado de Minas Gerais FAPEMIG - Brazil grant APQ-00782-21.
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The first author is supported by the CNPq-Brazil grant 406621/2021-7 and FAPEMIG-Brazil grant APQ-00782-21.
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Fernández Sare, H.D., Quintanilla, R. Moore Gibson Thompson thermoelastic plates: comparisons. J. Evol. Equ. 23, 70 (2023). https://doi.org/10.1007/s00028-023-00921-y
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DOI: https://doi.org/10.1007/s00028-023-00921-y