On certain mathematical models in continuum thermomechanics

  • V. G. Zvyagin
  • V. P. Orlov


This paper presents results on solvability of multidimensional systems of equations of thermoviscoelasticity. Both compressible and incompressible continua are considered. The existence and uniqueness of regular, weak, and weak-renormalized solutions are given, both local and global. The presented results are based on the successive approximation method combined with an a priori estimates, a fixed point argument and passage to the limit technique. The theory of anisotropic Sobolev spaces with a mixed norm and abstract differential equations are used.

Mathematics Subject Classification

Primary 80A17 Secondary 35Q35 


Thermoviscoelastic continuum a priori estimates successive approximations fixed point theorem weak solution weak-renormalized solution Oberbeck–Boussinesq-type system objective Jaumann derivative 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.Research Institute of MathematicsVoronezh State UniversityVoronezhRussia
  2. 2.Department of MathematicsVoronezh State UniversityVoronezhRussia

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