Abstract
We consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson (MGT) theory. First, we obtain the system of equations for such a case. Second, we consider the case of a rigid solid and show the existence and the exponential decay of solutions. Third, we consider the thermoelastic case and obtain the existence and the stability of the solutions. Exponential decay of solutions in the one-dimensional case is also recalled.
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Citation: FERNÁNDEZ, J. R. and QUINTANILLA, R. Moore-Gibson-Thompson theory for thermoelastic dielectrics. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-021-2703-9
J. R. FERNÁNDEZ has been partially funded by the Spanish Ministry de Science, Innovation and Universities (No. PGC2018-096696-B-I00, FEDER, UE).
R. QUINTANILLA has been funded by the Spanish Ministry of Economy and Competitiveness under the research project Análisis Matemático de Problemas de la Termomecánica (No. MTM2016-74934-P, AEI/FEDER, UE), and the Spanish Ministry de Science, Innovation and Universities under the research project Análisis matemático aplicado a la termomecánica (No. PID2019-105118GB-I00).
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Fernández, J.R., Quintanilla, R. Moore-Gibson-Thompson theory for thermoelastic dielectrics. Appl. Math. Mech.-Engl. Ed. 42, 309–316 (2021). https://doi.org/10.1007/s10483-021-2703-9
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DOI: https://doi.org/10.1007/s10483-021-2703-9