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


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.


Weak Solution Motion Equation Viscoelastic Medium Regularize Problem Incompressible Medium 
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  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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