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Moore-Gibson-Thompson theory for thermoelastic dielectrics

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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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References

  1. CIARLETTA, M. and IEŞAN, D. A theory of thermoviscoelastic dielectrics. Journal of Thermal Stresses, 14, 589–606 (1991)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  5. BAZARRA, N., FERNÁNDEZ, J. R., MAGAÑA, A., and QUINTANILLA, R. A porothermoelastic problem with dissipative heat conduction. Journal of Thermal Stresses, 43, 1415–1436 (2020)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  8. CONTI, M., PATA, V., PELLICER, M., and QUINTANILLA, R. On the analyticity of the MGT-viscoelastic plate with heat conduction. Journal of Differential Equations, 269, 7862–7880 (2020)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  13. QUINTANILLA, R. Moore-Gibson-Thompson thermoelasticity. Mathematics and Mechanics of Solids, 24, 4020–4031 (2019)

    Article  MathSciNet  Google Scholar 

  14. QUINTANILLA, R. Moore-Gibson-Thompson thermoelasticity with two temperatures. Applications in Engineering Science, 1, 100006 (2020)

    Article  Google Scholar 

  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)

    MATH  Google Scholar 

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Acknowledgements

The authors thank the anonymous reviewers whose comments have improved the final quality of the article.

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Authors and Affiliations

  1. Department of Applied Mathematics I, University of Vigo, Campus As Lagoas Marcosende, Vigo, 36310, Spain

    J. R. Fernández

  2. Department of Mathematics, Polytechnic University of Catalonia, Terrassa, 08222, Spain

    R. Quintanilla

Authors
  1. J. R. Fernández
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  2. R. Quintanilla
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Corresponding author

Correspondence to J. R. Fernández.

Additional information

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

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