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Nonlinear Thermoelasticity

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Thermoelastic Deformations

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 48))

Abstract

In this section we consider the equations of the nonlinear theory of thermoelastodynamics. In [92], Dafermos has established the continuous dependence of smooth thermodynamic processes upon the initial state and supply terms for nonconductors of heat. The results of Dafermos have been extended by Chirita [69] to heat-conducting elastic bodies. This section is devoted to the continuous dependence results given in [92], [69].

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Bibliographical Notes

  1. SLEMROD, M. Global existence, uniqueness, and asymptotic stability of classical smooth solutions in one-dimensional nonlinear thermoelasticity. Arch. Rational Mech. Anal., 76 (1981), 97–133.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. ZHENG, S. and SHEN, W. Global solutions to the Cauchy problem of quasi-linear hyperbolic parabolic coupled systems. Sci. Sinica, Ser. A, 30 (1987), 1133–1149.

    MathSciNet  MATH  Google Scholar 

  3. HRUSA, W.J. and TARABEK, M.A. On the smooth solutions of the Cauchy problem in one-dimensional nonlinear thermoelasticity. Quart. Appl. Math., 47 (1989), 631–644.

    MathSciNet  MATH  Google Scholar 

  4. RACKE, R. and SHIBATA, Y. Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity. Arch. Rational Mech. Anal., 116 (1991), 1–34.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. JIANG, S. Global existence of smooth solutions in one-dimensional nonlinear thermoelasticity. Proc. Roy. Soc. Edinburgh, 115 (1990), 257–274.

    Article  MATH  Google Scholar 

  6. DAFERMOS, C.M. and HSIAO, L. Development of singularities in solutions of the equations of nonlinear thermoelasticity. Quart. Appl. Math., 44 (1986), 463–474.

    MathSciNet  MATH  Google Scholar 

  7. HRUSA, W.J. and MESSAOUDI, S.A. On formation of singularities in one-dimensional nonlinear thermoelasticity. Arch. Rational Mech. Anal. 111 (1990), 135–152.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. FEIREISL, E. Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem. Comment. Math. Univ. Carolinae, 31 (1990), 243–255.

    MathSciNet  MATH  Google Scholar 

  9. RACKE, R. On the Cauchy problem in nonlinear 3-d-thermoelasticity. Math. Z., 203 (1990), 649–682.

    Article  MathSciNet  MATH  Google Scholar 

  10. RACKE, R. Blow-up in nonlinear three-dimensional thermoelasticity. Math. Meth. Appl. Sci., 12 (1990), 267–273.

    Article  MathSciNet  MATH  Google Scholar 

  11. JIANG, S. and RACKE, R. On some quasilinear hyperbolic-parabolic initial boundary value problems. Math. Meth. Appl. Sci., 12 (1990), 315–339.

    Article  MathSciNet  MATH  Google Scholar 

  12. CHRZESZCZYK, A. Some existence results in dynamical thermoelasticity. I. Nonlinear case. Arch. Mech., 39 (1987), 605–617.

    Google Scholar 

  13. JIANG, S. Far field behavior of solutions to the equations of nonlinear 1-dthermoelasticity. Appl. Anal., 36 (1990), 25–35.

    Article  MathSciNet  MATH  Google Scholar 

  14. JIANG, S. Rapidly decreasing behaviour of solutions in nonlinear 3-d-thermoelasticity. Bull. Austral. Math. Soc., 43 (1991), 89–99.

    Article  MathSciNet  Google Scholar 

  15. JIANG, S. A finite element method for equations of one-dimensional nonlinear thermoelasticity. J. Comp. Appl. Math. 21 (1988), 1–16.

    Article  MATH  Google Scholar 

  16. DE MOURA, C.A. and SUAIDEN, T. Termoelastodinamica nao-linear: experimentos numéricos em torno do modelo unidimensional de Slemrod. Atas II Journados Latino-Americanas de Matemâtica Aplicada, 1 (1983), 22–45.

    Google Scholar 

  17. RACKE, R. Mathematical Aspects in Nonlinear Thermoelasticity. SFB 256 Preprint No. 25, Universität Bonn, 1992.

    Google Scholar 

  18. WANG, C.C. and TRUESDELL, C. Introduction to Rational Elasticity. Leyden, Noordhoff, 1973.

    MATH  Google Scholar 

  19. IESAN, D. Asupra teoriei termoelasticitatii neliniare. An.,St. Univ. Iagi, Matematicä, 13 (1967), 161–175.

    Google Scholar 

  20. STOPPELLI, F. Sull’esistenza di soluzioni delle equazioni dell’elastostatica isoterma nel caso di sollecitazioni dotate di assi di equilibrio. Ricerche Mat., 6 (1957), 241–287; 7 (1958), 71–101; 138–152.

    Google Scholar 

  21. TRUESDELL, C. and NOLL, W. The Non-Linear Field Theories of Mechanics. In vol. III/3 of the Handbuch der Physik (Edited by S. Flügge) Berlin-Heidelberg-New York, Springer-Verlag, 1965.

    Google Scholar 

  22. WANG, C.C. and TRUESDELL, C. Introduction to Rational Elasticity. Leyden, Noordhoff, 1973.

    MATH  Google Scholar 

  23. NISTOR, I. A theorem of existence, uniqueness and analyticity of the solution of the equations of nonlinear thermoelasticity. An. St. Univ. “Al. I. Cuza”. Iasi, Matematica, 19 (1973), 465–476.

    Google Scholar 

  24. NAGHDI, P.M. The Theory of Shells and Plates. In “Handbuch der Physik”. vol. VI a/2. (Edited by C. Truesdell) Springer-Verlag, Berlin-HeidelbergNew York, 1972.

    Google Scholar 

  25. ANTMAN, S.S. The Theory of Rods. In vol. VI a/2 of Handbuch der Physik (Edited by C. Truesdell ), Springer-Verlag, Berlin-Heidelberg-New York, 1972.

    Google Scholar 

  26. KEENE, F.W. and HETNARSKI, R.B. Bibliography on thermal stresses in shells. J. Thermal Stresses, 13 (1990), 341–540.

    MathSciNet  Google Scholar 

  27. KNOPS, R.J. and WILKES, E.W. Theory of Elastic Stability. pp. 125–302 of Flügge’s Handbuch der Physik, vol. VI a/3 (Edited by C. Truesdell) Springer-Verlag, Berlin-Heidelberg-New York, 1973.

    Google Scholar 

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Ieşan, D., Scalia, A. (1996). Nonlinear Thermoelasticity. In: Thermoelastic Deformations. Solid Mechanics and Its Applications, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3517-9_5

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  • DOI: https://doi.org/10.1007/978-94-017-3517-9_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4752-6

  • Online ISBN: 978-94-017-3517-9

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