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Nonlocal problems for filtration equations for nonNewtonian fluids in a porous medium

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Abstract

The following nonlocal problems are studied for the filtration equations of 1) an Oldroyd fluid and 2) of a Kelvin-Voigt fluid: the existence of solutions for the initial boundary problems for the semiaxis t>0 with free terms

and the existence of solution periodic in t with period ω with free terms

which are also periodic in t with period ω.

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Literature cited

  1. A. P. Oskolkov and M. M. Akhmatov, in: Problems of the Quantum Theory of Fields and Statistical Physics, VI, Zap. Nauchn. Sem. LOMI, Vol. 150 (1986), pp. 130–141.

    Google Scholar 

  2. A. P. Oskolkov, M. M. Akhmatov, and A. A. Kotsiolis, in: Boundary Problems of Mathematical Physics and Continuous Problems of the Theory of Functions, 19, Zap. Nauchn. Sem. LOMI, Vol. 163 (1987), pp. 101–107.

    Google Scholar 

  3. A. A. Akhmatov, Author's Abstract, Candidate's Dissertation [in Russian], Leningrad (1990).

  4. J. L. Lions, Some Methods of Solving Nonlinear Boundary Problems [Russian translation], Moscow (1967).

  5. O. A. Ladyzhenskaya, Mathematical Problems of the Dynamics of Viscous Incompressible Fluids [in Russian], 2nd ed., Moscow (1970).

  6. O. A. Ladyzhenskaya, Boundary Problems of Mathematical Physics [in Russian], Moscow (1974).

  7. A. P. Oskolkov and R. D. Shadiev, in: Differential Geometry, Lie Groups and Mechanics, XI. Zap. Nauchn. Semin. LOMI, Vol. 181 (1990), pp. 122–163.

    Google Scholar 

  8. A. P. Oskolkov and R. D. Shadiev, in: Analytical Theory of Numbers and the Theory of Functions, 10, Zap. Nauch. Sem. LOMI, Vol. 185 (1990), pp. 134–148.

    Google Scholar 

  9. R. D. Shadiev, Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 6, 17–24 (1990).

    Google Scholar 

  10. R. D. Shadiev, Preprint LOMI R-6-90 [in Russian], Leningrad (1990).

  11. A. P. Oskolkov and R. D. Shadiev, in: Boundary Problems of Mathematical Physics and Contiguous Problems of the Theory of Functions, 22, Zap. Nauchn. Sem. LOMI, Vol. 188 (1990), pp. 85–108.

    Google Scholar 

  12. J. Serrin, Arch. Rat. Mech. Anal.,3, No. 1, 1–3 (1959);3, No. 3, 20–22 (1959).

    Google Scholar 

  13. A. A. Kotsiolis, A. P. Oskolkov, and R. D. Shadiev, Preprint LOMI R-10-89 [in Russian], Leningrad (1989).

  14. A. A. Kotsiolis, A. P. Oskolkov, and R. D. Shadiev, in: Bounary Problems of Mathematical Physics and Contiguous Problems of the Theory of Functions, 21, Zap. Nauchn. Sem. LOMI, Vol. 182 (1990), pp. 86–101.

    Google Scholar 

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Authors
  1. A. P. Oskolkov
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  2. M. M. Akhmatov
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  3. R. D. Shadiev
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 189, pp. 82–100, 1991.

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Oskolkov, A.P., Akhmatov, M.M. & Shadiev, R.D. Nonlocal problems for filtration equations for nonNewtonian fluids in a porous medium. J Math Sci 62, 2992–3004 (1992). https://doi.org/10.1007/BF01097498

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  • DOI: https://doi.org/10.1007/BF01097498

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