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.
J. R. FERNÁNDEZ, R. QUINTANILLA
. Moore-Gibson-Thompson theory for thermoelastic dielectrics[J]. Applied Mathematics and Mechanics, 2021
, 42(2)
: 309
-316
.
DOI: 10.1007/s10483-021-2703-9
[1] CIARLETTA, M. and IEŞAN, D. A theory of thermoviscoelastic dielectrics. Journal of Thermal Stresses, 14, 589-606(1991)
[2] GURTIN, M. E. Time-reversal and symmetry in the thermodynamics of materials with memory. Archive for Rational Mechanics and Analysis, 44, 387-399(1972)
[3] BORGHESANI, R. and MORRO, A. Relaxation functions and time-reversal invariance in thermal and electric conduction. Annali di Matematica Pura ed Applicata, 114, 271-288(1977)
[4] BORGHESANI, R. and MORRO, A. Time-reversal invariance in thermodynamics of electromagnetic fields in materials with memory. Annali di Matematica Pura ed Applicata, 99, 65-80(1974)
[5] BAZARRA, N., FERNÁNDEZ, J. R., MAGAÑA, A., and QUINTANILLA, R. A poro-thermoelastic problem with dissipative heat conduction. Journal of Thermal Stresses, 43, 1415-1436(2020)
[6] BAZARRA, N., FERNÁNDEZ, J. R., and QUINTANILLA, R. Analysis of a Moore-Gibson-Thompson thermoelastic problem. Journal of Computational and Applied Mathematics, 382, 113058(2021)
[7] CONTI, M., PATA, V., and QUINTANILLA, R. Thermoelasticity of Moore-Gibson-Thompson type with history dependence in temperature. Asymptotic Analysis, 120, 1-21(2020)
[8] CONTI, M., PATA, V., PELLICER, M., and QUINTANILLA, R. On the analyticity of the MGTviscoelastic plate with heat conduction. Journal of Differential Equations, 269, 7862-7880(2020)
[9] JANGID, K. and MUKHOPADHYAY, S. A domain of influence theorem under MGT thermoelasticity theory. Mathematics and Mechanics of Solids (2020) https://doi.org/10.1177/1081286520946820
[10] JANGID, K. and MUKHOPADHYAY, S. A domain of influence theorem for a natural stress-heat-flux problem in the MGT thermoelasticity theory. Acta Mechanica (2020) https://doi.org/10.1007/s00707-020-02833-1
[11] KUMAR, H. and MUKHOPADHYAY, S. Thermoelastic damping analysis in microbeam resonators based on Moore-Gibson-Thompson generalized thermoelasticity theory. Acta Mechanica, 231, 3003-3015(2020)
[12] PELLICER, M. and QUINTANILLA, R. On uniqueness and instability for some thermomechanical problems involving the Moore-Gibson-Thompson equation. Journal of Applied Mathematics and Physics, 71, 84(2020)
[13] QUINTANILLA, R. Moore-Gibson-Thompson thermoelasticity. Mathematics and Mechanics of Solids, 24, 4020-4031(2019)
[14] QUINTANILLA, R. Moore-Gibson-Thompson thermoelasticity with two temperatures. Applications in Engineering Science, 1, 100006(2020)
[15] LIU, Z. and ZHENG, S. Semigroups Associated With Dissipative Systems, Chapman & Hall/CRC Research Notes in Mathematics, Vol. 398, Chapman & Hall/CRC, Boca Raton, FL (1999)
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