Encyclopedia of Thermal Stresses

2014 Edition
| Editors: Richard B. Hetnarski

Existence and Uniqueness: Solutions of Thermoelastodynamics

  • Maria Grazia Naso
Reference work entry
DOI: https://doi.org/10.1007/978-94-007-2739-7_535



We are concerned with a linear one-dimensional thermoelastic system where the hyperbolic elastic system is joined with the parabolic heat equation. In order to study the well posedness of the associated initial boundary value problem, a basic procedure is analyzed by means of semigroup techniques. For a detailed study in more general cases, some references are given at the end of this section.

A Simple Model in Thermoelasticity

The One-Dimensional Linear Thermoelastic System

For \( T>0 \)
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Further Reading

  1. Bonfanti G, Muñoz Rivera JE, Naso MG (2008) Global existence and exponential stability for a contact problem between two thermoelastic beams. J Math Anal Appl 345(1):186–202zbMATHMathSciNetGoogle Scholar
  2. Bonfanti G, Fabrizio M, Muñoz Rivera JE, Naso MG (2010) On the energy decay for a thermoelastic contact problem involving heat transfer. J Therm Stresses 33(11):1049–1065Google Scholar
  3. Chiriţă S, Ciarletta M (2010) Spatial behavior for some non-standard problems in linear thermoelasticity without energy dissipation. J Math Anal Appl 367(1):58–68zbMATHMathSciNetGoogle Scholar
  4. Ciarletta M (2002) On the uniqueness and continuous dependence of solutions in dynamical thermoelasticity backward in time. J Therm Stresses 25(10):969–984MathSciNetGoogle Scholar
  5. Ciarletta M, Scalia A (1994) Theory of thermoelastic dielectrics with voids. J Therm Stresses 17(4):529–548MathSciNetGoogle Scholar
  6. Ciarletta M, Scalia A, Svanadze M (2007) Fundamental solution in the theory of micropolar thermoelasticity for materials with voids. J Therm Stresses 30(3):213–229MathSciNetGoogle Scholar
  7. Ciarletta M, Svanadze M, Buonanno L (2009) Plane waves and vibrations in the theory of micropolar thermoelasticity for materials with voids. Eur J Mech A Solids 28(4):897–903zbMATHMathSciNetGoogle Scholar
  8. Henry DB, Perissinitto A Jr, Lopes O (1993) On the essential spectrum of a semigroup of thermoelasticity. Nonlinear Anal 21(1):65–75zbMATHMathSciNetGoogle Scholar
  9. Jiang S (1992) Global solutions of the Neumann problem in one-dimensional nonlinear thermoelasticity. Nonlinear Anal 19(2):107–121MathSciNetGoogle Scholar
  10. Kawashima S, Shibata Y (1995) On the Neumann problem of one-dimensional nonlinear thermoelasticity with time-independent external forces. Czechoslovak Math J 45(120/1):39–67zbMATHMathSciNetGoogle Scholar
  11. Muñoz Rivera JE, Qin Y (2002) Global existence and exponential stability in one-dimensional nonlinear thermoelasticity with thermal memory. Nonlinear Anal 51(1):11–32, Ser. A: Theory MethodszbMATHMathSciNetGoogle Scholar
  12. Racke R (1986) Eigenfunction expansions in thermoelasticity. J Math Anal Appl 120(2):596–609zbMATHMathSciNetGoogle Scholar
  13. Racke R (1988) Initial boundary value problems in one-dimensional nonlinear thermoelasticity. Math Meth Appl Sci 10(5):517–529zbMATHMathSciNetGoogle Scholar
  14. Racke R, Shibata Y (1991) Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity. Arch Ration Mech Anal 116(1):1–34zbMATHMathSciNetGoogle Scholar
  15. Racke R, Shibata Y, Zheng S (1993) Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity. Quart Appl Math 51(4):751–763zbMATHMathSciNetGoogle Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Università degli Studi di BresciaBresciaItaly