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Time-Nonlocal Boundary Value Problem for Degenerate Sobolev Type Equations

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We establish the solvability of time-nonlocal boundary value problems for degenerate Sobolev type equations with an elliptic-parabolic second order operator at the timederivative. We prove the uniqueness of a regular solution. Bibliography: 10 titles.

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References

  1. A. I. Kozhanov, “Certain classes of degenerate Sobolev–Galpern equation” [in Russian], Siberian Adv. Math. 4, No. 1, 65–94 (1994).

  2. A. I. Kozhanov, “Parabolic equations with nonlocal nonlinear source” [in Russian], Sib. Mat. Zh. 35, No. 5, 1062–1073 (1994); English transl.: Sib. Math. J. 35, No. 5, 945–956 (1994).

  3. N. R. Pinigina, “The boundary-value problem for degenerate ultraparabolic equations of the Sobolev type” [in Russian], Izv. Vyssh. Uchebn. Zaved., Mat. No. 4, 65–73 (2012); English transl.: Rus. Math. 56, No. 4, 54–61 (2012).

  4. N. R. Pinigina, “Boundary value problem for a class of degenerate Sobolev type systems” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 12, No. 3, 127–138 (2012); English transl.: J. Math. Sci., New York 202, No. 1, 80–90 (2014).

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  6. A. M. Nakhushev, Loaded Equations and Their Applications [in Russian], Nauka, Moscow (2012).

  7. M. T. Dzhenaliev, A Remark on the Theory of Linear Boundary Value Problems for Loaded Differential Equations [in Russian], Computer Center, Alma Aty (1995).

  8. S. Ya. Yakubov, Linear Differential-Operator Equations and Applications [in Russian], Elm, Baku (1985).

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Authors and Affiliations

  1. M. K. Ammosov North-Eastern Federal University, 58, Belinskogo St., Yakutsk, 677000, Russia

    N. R. Pinigina

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  1. N. R. Pinigina
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Correspondence to N. R. Pinigina.

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Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 14, No. 2, 2014, pp. 49-62.

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Pinigina, N.R. Time-Nonlocal Boundary Value Problem for Degenerate Sobolev Type Equations. J Math Sci 211, 811–823 (2015). https://doi.org/10.1007/s10958-015-2636-6

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  • DOI: https://doi.org/10.1007/s10958-015-2636-6

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