Moore-Gibson-Thompson theory for thermoelastic dielectrics

doi:10.1007/s10483-021-2703-9

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (2): 309-316.doi: https://doi.org/10.1007/s10483-021-2703-9

• 论文 • 上一篇

Moore-Gibson-Thompson theory for thermoelastic dielectrics

J. R. FERNÁNDEZ¹, R. QUINTANILLA²

1. Department of Applied Mathematics I, University of Vigo, Campus As Lagoas Marcosende, Vigo 36310, Spain;
2. Department of Mathematics, Polytechnic University of Catalonia, Terrassa 08222, Spain

收稿日期:2020-08-24 修回日期:2020-11-30 发布日期:2021-01-30
通讯作者: J. R. FERNÁNDEZ E-mail:jose.fernandez@uvigo.es

Moore-Gibson-Thompson theory for thermoelastic dielectrics

J. R. FERNÁNDEZ¹, R. QUINTANILLA²

1. Department of Applied Mathematics I, University of Vigo, Campus As Lagoas Marcosende, Vigo 36310, Spain;
2. Department of Mathematics, Polytechnic University of Catalonia, Terrassa 08222, Spain

Received:2020-08-24 Revised:2020-11-30 Published:2021-01-30
Contact: J. R. FERNÁNDEZ E-mail:jose.fernandez@uvigo.es

摘要/Abstract

摘要： 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.

关键词: Moore-Gibson-Thompson (MGT) thermoelastic dielectrics, existence, semigroup, exponential decay

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.

Key words: Moore-Gibson-Thompson (MGT) thermoelastic dielectrics, existence, semigroup, exponential decay

中图分类号:

37N15
74F05

J. R. FERNÁNDEZ, R. QUINTANILLA. Moore-Gibson-Thompson theory for thermoelastic dielectrics[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(2): 309-316.

参考文献

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[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)
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[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)
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Moore-Gibson-Thompson theory for thermoelastic dielectrics

Moore-Gibson-Thompson theory for thermoelastic dielectrics

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