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Journal of Mathematical Sciences

, Volume 170, Issue 5, pp 629–641 | Cite as

On the energy approach and thermodynamic foundations of the variational formulation of boundary-value problems of thermomechanics with regard for near-surface phenomena

  • Ya. I. Burak
  • H. I. Moroz
  • Z. V. Boiko
Article

Within the framework of the energy, thermodynamic, and variational approaches, we propose a mathematical model for the description of thermomechanical processes in elastic deformable systems with regard for dissipative effects in the formation of near-surface phenomena. On the basis of a combination of the energy and thermodynamic approaches, we have obtained relations for the local thermodynamic state and the description of dissipative processes. Using the variational approach, we have constructed a functional such that, from the conditions of its minimization, one can obtain the above-mentioned relations for local thermodynamic state and the description of dissipative processes as well as natural boundary conditions. The sufficient conditions of convexity of this functional have been formulated.

Keywords

Variational Formulation Dissipative Process Elastic System Thermodynamic Approach Energy Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • Ya. I. Burak
    • 1
  • H. I. Moroz
    • 1
  • Z. V. Boiko
    • 1
  1. 1.Center of Mathematical Modeling, Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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