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Journal of Mathematical Sciences

, Volume 144, Issue 5, pp 4398–4408 | Cite as

On the convergence of solutions of the regularized problem for motion equations of Jeffreys viscoelastic medium to solutions of the original problem

  • D. A. Vorotnikov
  • V. G. Zvyagin
Article

Abstract

In this work, we consider initial-boundary-value problems for motion equations of a viscoelastic medium with the Jeffreys constitutive law and for motion equations of the regularized Jeffreys model. We obtain a theorem on the convergence of weak solutions of initial-boundary-value problems for the regularized model to weak solutions of the original problem as the regularization parameter tends to zero.

Keywords

Weak Solution Motion Equation Viscoelastic Medium Regularize Problem Incompressible Medium 
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References

  1. 1.
    V. T. Dmitrienko and V. G. Zvyagin, “Investigation of a regularized model of motion of a viscoelastic medium,” in: O. Rozanova, ed., Analytical Approaches to Multidimensional Balance Laws, Nova Science, New York (2004).Google Scholar
  2. 2.
    R. V. Goldstein and V. A. Gorodtsov, Mechanics of Continuous Media, Part I [in Russian], Nauka, Fizmatlit, Moscow (2000).Google Scholar
  3. 3.
    C. Guillopé and J. C. Saut, “Mathematical problems arising in differential models for viscoelastic fluids,” in: Mathematical Topics in Fluid Mechanics, Longman, Harlow (1993), pp. 64–92.Google Scholar
  4. 4.
    W. G. Litvinov, A Model and General Problem on Plastic Flow under Deformations, Bericht, Universität Stuttgart (1999).Google Scholar
  5. 5.
    J. G. Oldroyd, “Non-Newtonian flow of fluids and solids,” in: F. R. Eirich, ed., Rheology: Theory and Applications, Academic Press (1956).Google Scholar
  6. 6.
    M. Reiner, “Rheology,” in: S. Flugge, ed., Handbuch der Physik, Bd. VI, Springer (1958).Google Scholar
  7. 7.
    R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland (1979).Google Scholar
  8. 8.
    D. A. Vorotnikov and V. G. Zvyagin, “On the existence of weak solutions for the initial-boundary value problem in the Jeffreys model of motion of a viscoelastic medium,” Abstr. Appl. Anal., 10, 815–829 (2004).CrossRefGoogle Scholar
  9. 9.
    V. G. Zvyagin and V. T. Dmitrienko, “On the weak solutions of the regularized model of a viscoelastic fluid,” Differ. Uravn., 38, No. 12, 1633–1645 (2002).Google Scholar
  10. 10.
    V. G. Zvyagin and D. A. Vorotnikov, Mathematical Models of Non-Newtonian Fluids [in Russian], VSU, Voronezh (2004).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • D. A. Vorotnikov
    • 1
  • V. G. Zvyagin
    • 1
  1. 1.Voronezh State UniversityRussia

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