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Journal of Mathematical Sciences

, Volume 226, Issue 1, pp 11–27 | Cite as

Well-Posedness of the Green–Lindsay Variational Problem of Dynamic Thermoelasticity

  • І. А. Chyr
  • H. A. Shynkarenko
Article

On the basis of the Green–Lindsay initial-boundary-value problem of thermoelasticity, we formulate the corresponding variational problem in terms of displacements and temperature. Sufficient conditions of regularity of the initial data of the problem and the uniqueness of its solution are established from the energy equation of the variational problem. To prove the existence of the generalized solution (and simultaneously, as the first step to a well-justified procedure for finding its approximation), we use the method of Galerkin semidiscretization with respect to the spatial variables and show that the limit of the sequence of its approximations is the solution of the Green–Lindsay variational problem.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • І. А. Chyr
    • 1
  • H. A. Shynkarenko
    • 1
    • 2
  1. 1.Franko Lviv National UniversityLvivUkraine
  2. 2.Politechnika OpolskaOpolePoland

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