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A final boundary problem for modeling a thermoelastic Cosserat body

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Abstract

In this study, we consider the final boundary value problem for a thermoelastic Cosserat material. With the help of a simple translation, our final problem is transformed in a usual mixed problem with boundary relations and initial data. For this new problem, we obtain some theorems of uniqueness of solutions. For this, we do not use any law of conservation of energy, as is usually done to obtain a result of uniqueness. Moreover, we do not need assumptions to ensure the boundedness of the tensors which characterize thermoelastic coefficients.

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References

  1. Ames, K.A., Payne, L.E.: Stabilizing solutions of the equations of dynamical linear thermoelasticity backward in time. Stab. Appl. Anal. Contin. 1, 243–260 (1991)

    MathSciNet  Google Scholar 

  2. Bhatti, M.M., et al.: Swimming of Gyrotactic Microorganism in MHD Williamson nanofluid flow between rotating circular plates embedded in porous medium: application of thermal energy storage. J Energy Storage, 45(2022), Art. No. 103511

  3. Bhatti, M.M., et al.: Heat transfer effects on electro-magnetohydrodynamic Carreau fluid flow between two micro-parallel plates with Darcy–Brinkman–Forchheimer medium. Arch. Appl. Mech. 91(4), 1683–95 (2021)

    Article  ADS  Google Scholar 

  4. Brun, L.: Methodes energetiques dans les systemes lineaires. J. Mecanique 8, 167–192 (1969)

    MATH  Google Scholar 

  5. Ciarletta, M., Chirita, S.: Spatial behavior in linear thermoelasticity backward in time. In: Chao, C.K., Lin, C.Y. (eds) Proceedings of the Fourth International Congress on Thermal Stresses, Osaka, Japan, pp. 485–488 (2001)

  6. Ciarletta, M.: On the bending of microstretch elastic plates. Int. J. Eng. Sci. 37, 1309–1318 (1995)

    Article  MathSciNet  Google Scholar 

  7. Ciarletta, M.: On the uniqueness and continuous dependence of solutions in dynamical thermoelasticity backward in time. J. Therm. Stresses 25, 969–984 (2002)

    Article  MathSciNet  Google Scholar 

  8. Eringen, A.C.: Theory of micromorphic materials with memory. Int. J. Eng. Sci. 10, 623–641 (1972)

    Article  Google Scholar 

  9. Eringen, A.C.: Theory of thermo-microstretch elastic solids. Int. J. Eng. Sci. 28, 1291–1301 (1990)

    Article  Google Scholar 

  10. Eringen, A.C.: Microcontinuum Field Theories. Springer, New York (1999)

    Book  Google Scholar 

  11. Green, A.E., Laws, N.: On the entropy production inequality. Arch. Rat. Mech. Anal. 45, 47–59 (1972)

    Article  MathSciNet  Google Scholar 

  12. Groza, G., Pop, N.: Approximate solution of multipoint boundary value problems for linear differential equations by polynomial functions. J. Differ. Equ. Appl. 14(12), 1289–1309 (2008)

    Article  MathSciNet  Google Scholar 

  13. Iesan, D., Pompei, A.: Equilibrium theory of microstretch elastic solids. Int. J. Eng. Sci. 33, 399–410 (1995)

    Article  MathSciNet  Google Scholar 

  14. Iesan, D., Quintanilla, R.: Thermal stresses in microstretch bodies. Int. J. Eng. Sci. 43, 885–907 (2005)

    Article  Google Scholar 

  15. Iovane, G., Passarella, F.: Spatial behaviour in dynamical thermoelasticity backward in time for porous media. J. Therm. Stresses 27, 97–109 (2004)

    Article  Google Scholar 

  16. Knops, K.J., Payne, L.E.: On uniqueness and continuous data dependence in dynamical problems of linear thermoelasticity. Int. J. Solids Struct. 6, 1173–1184 (1970)

    Article  Google Scholar 

  17. Koch, H., Lasiecka, I.: Backward uniqueness in linear thermoelasticity with time and space variable coefficients, In: Functional analysis and evolution equations: Gunter Lumer volume. Birkhäuser, Basel, pp. 389–403 (2007)

  18. Levine, H.A.: On a theorem of Knops and Payne in dynamical thermoelasticity. Arch. Ration. Mech. Anal. 38, 290–307 (1970)

    Article  Google Scholar 

  19. Marin, M.: A temporally evolutionary equation in elasticity of micropolar bodies with voids, U.P.B. Sci. Bull. Series A-Appl. Math. Phys. 60 (3–4), 3–12 (1998)

  20. Marin, M.: On weak solutions in elasticity of dipolar bodies with voids. J. Comput. Appl. Math. 82(1–2), 291–297 (1997)

    Article  MathSciNet  Google Scholar 

  21. Marin, M., et al.: A domain of influence in the Moore–Gibson–Thompson theory of dipolar bodies. J. Taibah Univ. Sci. 14(1), 653–660 (2020)

    Article  Google Scholar 

  22. Marin, M., Öchsner, A.: The effect of a dipolar structure on the Hölder stability in Green–Naghdi thermoelasticity. Contin. Mech. Thermodyn. 29(6), 1365–1374 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  23. Marin, M., Öchsner, A.: Essential of Partial Differential Equations. Springer, Cham (2019)

    Book  Google Scholar 

  24. Othman, M.I.A., et al.: A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase-lag model. Int. J. Numer. Method H 29(12), 4788–4806 (2019)

    Article  Google Scholar 

  25. Othman, M.I.A., Marin, M.: Effect of thermal loading due to laser pulse on thermo-elastic porous medium under G-N theory. Results Phys. 7, 3863–3872 (2017)

    Article  ADS  Google Scholar 

  26. Pop, N., et al.: A finite element method used in contact problems with dry friction, Comput. Mater. Sci., 50(4), 1283–1285 (2011)

  27. Vlase, S., et al.: A method for the study of the vibration of mechanical bars systems with symmetries. Acta Tech. Napocensis, Ser. Appl. Math. Mech. Eng., 60(4), 539–544 (2017)

  28. Vlase, S., et al.: Elasto-dynamics of a solid with a general “Rigid” motion using FEM model. Part II. analysis of a double cardan joint. Rom. J. Phys., 58 (7–8), 882–892 (2013)

  29. Wilkes, N.S.: Continuous dependence and instability in linear thermoelasticity. SIAM J. Appl. Math. 11, 292–299 (1980)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036, Brasov, Romania

    Marin Marin

  2. Faculty of Mechanical and Systems Engineering, Esslingen University of Applied Sciences, 73728, Esslingen, Germany

    Andreas Öchsner

  3. Department of Mechanical Engineering, Transilvania University of Brasov, 500036, Brasov, Romania

    Sorin Vlase

Authors
  1. Marin Marin
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  2. Andreas Öchsner
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  3. Sorin Vlase
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Correspondence to Marin Marin.

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Communicated by Andreas Öchsner.

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Marin, M., Öchsner, A. & Vlase, S. A final boundary problem for modeling a thermoelastic Cosserat body. Continuum Mech. Thermodyn. 34, 627–636 (2022). https://doi.org/10.1007/s00161-022-01083-x

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  • DOI: https://doi.org/10.1007/s00161-022-01083-x

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