Geodesic
On the convergence of solutions of regularized problem for motion equations of Jeffreys viscoelastic medium to solutions of the original problem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 49-63.

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In this work, we consider initial-boundary-value problems for motion equations of 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. 
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D. A. Vorotnikov; V. G. Zvyagin. On the convergence of solutions of regularized problem for motion equations of Jeffreys viscoelastic medium to solutions of the original problem. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 49-63. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a3/

[1] Goldshtein R. V., Gorodtsov V. A., Mekhanika sploshnykh sred. Chast I, Nauka, Fizmatlit, 2000

[2] Zvyagin V. G., Vorotnikov D. A., Matematicheskie modeli nenyutonovskikh zhidkostei, VGU, Voronezh, 2004

[3] Zvyagin V. G., Dmitrienko V. T., “O slabykh resheniyakh regulyarizovannoi modeli vyazkouprugoi zhidkosti”, Differents. uravn., 38:12 (2002), 1633–1645 | MR | Zbl

[4] Oldroid Dzh. G., “Nenyutonovskie techeniya zhidkostei i tverdykh tel”, Reologiya: Teoriya i prilozheniya, IL, M., 1962, 757–793

[5] Reiner M., Reologiya, Fizmatgiz, M., 1965

[6] Temam R., Uravneniya Nave–Stoksa, Mir, M., 1981 | MR | Zbl

[7] Dmitrienko V. T., Zvyagin V. G., “Investigation of a regularized model of motion of a viscoelastic medium”, Analytical Approaches to Multidimensional Balance Laws, ed. O. Rozanova, Nova Science, New York, 2004 | MR

[8] Guillopé C., Saut J. C., “Mathematical problems arising in differential models for viscoelastic fluids”, Mathematical Topics in Fluid Mechanics, Longman, Harlow, 1993, 64–92 | MR | Zbl

[9] Litvinov W. G., A model and general problem on plastic flow under deformations Bericht, Universität Stuttgart, 1999

[10] Vorotnikov D. A., Zvyagin V. G., “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., 2004, no. 10, 815–829 | DOI | MR | Zbl