Advertisement

Meccanica

, Volume 53, Issue 14, pp 3607–3613 | Cite as

Some qualitative results for a modification of the Green–Lindsay thermoelasticity

  • R. QuintanillaEmail author
Brief Notes and Discussions

Abstract

In this short note we consider a recent modification of the Green–Lindsay thermoelastic theory proposed at Yu et al. (Meccanica 53:2543–2554, 2018). We consider a functional defined on the solutions of the problem. It allows us to obtain the continuous dependence of the solutions with respect to the initial conditions and to the supply terms, the time exponential decay of solutions and an alternative of Phragmén–Lindelöf type for the spatial behaviour.

Keywords

Modified Green–Lindsay thermoelasticity Continuous dependence Uniqueness Exponential decay Spatial behaviour 

Notes

Acknowledgements

The investigation reported in this paper is supported by the project project “Análisis Matemático de Problemas de la Termomecánica” (MTM2016-74934-P)(AEI/FEDER, UE) of the Spanish Ministry of Economy and Competitiveness. The author thanks to the anonymous referee his useful suggestions concerning this submission.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.

References

  1. 1.
    Bofill F, Quintanilla R (1995) Some qualitative results for the theory of thermo-microstretch elastic solids. Int J Eng Sci 33:2115–2125MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cattaneo C (1948) Sulla conduzioini del calore. Atti Semin Mat Fis Univ Modena 3:83–101zbMATHGoogle Scholar
  3. 3.
    Chirita S (1995) Saint-Venant’s principle in linear elasticity. J Thermal Stress 18:485–496CrossRefGoogle Scholar
  4. 4.
    Flavin JN, Knops RJ, Payne LE (1989) Decay estimates for the constrained elastic cylinder of variable cross-section. Q Appl Math 47:325–350MathSciNetCrossRefGoogle Scholar
  5. 5.
    Green AE, Lindsay K (1972) Thermoelasticity. J Elast 2:1–7CrossRefGoogle Scholar
  6. 6.
    Green AE, Naghdi PM (1992) On undamped heat waves in elastic solids. J Thermal Stress 15:252–264ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Green AE, Naghdi PM (1993) Thermoelasticity without energy dissipation. J Elast 31:189–208MathSciNetCrossRefGoogle Scholar
  8. 8.
    Horgan CO, Quintanilla R (2005) Spatial behaviour of solutions of the dual-phase-lag heat equation. Math Methods Appl Sci 28:43–57MathSciNetCrossRefGoogle Scholar
  9. 9.
    Iesan D, Quintanilla R (2000) On a theory of thermoelasticity with microtemperatures. J Thermal Stress 23:199–216MathSciNetCrossRefGoogle Scholar
  10. 10.
    Jun Yu Y, Xue Z-N, Tian X-G (2018) A modified Green–Lindsay thermoelastidcity with strain rate to eliminate discontinuity. Meccanica 53:2543–2554MathSciNetCrossRefGoogle Scholar
  11. 11.
    Leseduarte MC, Magaña A, Quintanilla R (2010) On the time decay of solutions in porous-thermo-elasticity of type II. Discrete Contin Dyn Syst Ser B 13:375–391MathSciNetCrossRefGoogle Scholar
  12. 12.
    Leseduarte MC, Quintanilla R (2014) On the spatial behavior in type III thermoelastodynamics. J Appl Math Phys (ZAMP) 65:165–177MathSciNetCrossRefGoogle Scholar
  13. 13.
    Leseduarte MC, Quintanilla R (2018) Spatial behavior in high order partial differential equations. Math Methods Appl Sci 41:2480–2493MathSciNetzbMATHGoogle Scholar
  14. 14.
    Lord H, Shulman Y (1967) A generalized dynamic theory of thermoelasticity. J Mech Phys Solids 15:299–309ADSCrossRefGoogle Scholar
  15. 15.
    Navarro CB, Quintanilla R (1984) On existence and uniquenes in incremental thermoelasticity. J Appl Math Phys (ZAMP) 35:206–215CrossRefGoogle Scholar
  16. 16.
    Quintanilla R (2001) End effects in thermoelasticity. Math Methods Appl Sci 24:93–102MathSciNetCrossRefGoogle Scholar
  17. 17.
    Quintanilla R, Racke R (2003) Stability in thermoelasticity of type III. Discrete Contin Dyn Syst B 3:383–400MathSciNetCrossRefGoogle Scholar
  18. 18.
    Quintanilla R, Straughan B (2000) Growth and uniqueness in thermoelasticity. Proc R Soc Lond Ser A 456:1419–1429ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Saint-Venant AJCB (1853) Mémoire sur la torsion des prismes. In: Mémoires présentés pour divers Savants a Ácadémie des Sciences de l’Institut Impérial de France, vol 14, pp 233–560Google Scholar
  20. 20.
    Saint-Venant AJCB (1856) Mémoire sur la flexion des prismes. J Math Pures Appl 1(Ser. 2):89–189Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Matemàtiques, ESEIAATUniversitat Politècnica de CatalunyaBarcelonaSpain

Personalised recommendations