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On the Solvability of Boundary-Value Problems with Continuous and Generalized Gluing Conditions for the Equation of Mixed Type with Loaded Term

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We study the unique solvability of boundary-value problems with normal derivatives and continuous and generalized gluing conditions for a loaded equation of the third order.

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References

  1. 1.

    A. M. Nakhushev, Equations of Mathematical Biology [in Russian], Vysshaya Shkola, Moscow (1995).

  2. 2.

    M. T. Dzhenaliev, On the Theory of Linear Boundary-Value Problems for Loaded Differential Equations [in Russian], Institute of Theoretical and Applied Mathematics, Kazakhstan National Academy of Sciences, Alma-Ata (1995).

  3. 3.

    A. I. Kozhanov, “Nonlinear loaded equations and inverse problems,” Zh. Vychisl. Mat. Mat. Fiz., 44, No. 4 (2004).

  4. 4.

    A. M. Nakhushev, “Loaded equations and their applications,” Differents. Uravn., 19, No. 1, 86–94 (2004).

  5. 5.

    J. Wiener and L. Debnath, “Partial differential equations with piecewise constant delay,” Int. J. Math. Math. Sci., 14, 485–496 (1991).

  6. 6.

    A.V. Bitsadze and M. S. Salakhitdinov, “On the theory of equations of mixed-combined type,” Sib. Mat. Zh., 2, No. 1, 7–19 (1961).

  7. 7.

    T. D. Dzhuraev, Boundary-Value Problems for Equations of Mixed and Mixed-Combined Types [in Russian], Fan, Tashkent (1979).

  8. 8.

    A. I. Kozhanov, Boundary-Value Problems for Nonclassical Equations of Mathematical Physics of Odd Order [in Russian], Novosibirsk State University, Novosibirsk (1990).

  9. 9.

    K. B. Sabitov, “On one boundary-value problem for the equation of mixed type of the third order,” Dokl. Akad. Nauk, 427, No. 5, 593–596 (2009).

  10. 10.

    V. A. Eleev, “Some boundary-value problems for mixed loaded equations of the second and third orders,” Differents. Uravn., 30, No. 2, 230–237 (1994).

  11. 11.

    V. A. Eleev and A. M. Laipanova, “Boundary-value problem for a mixed loaded hyperbolic-parabolic-type equation of the third order,” Vestn. Samarkand. Gos. Univ., No. 2, 14–22 (2003).

  12. 12.

    B. Islomov and D. M. Kur’yazov, “Boundary-value problems for a mixed loaded hyperbolic-parabolic-type equation of the third order,” Uzb. Mat. Zh., No. 2, 29–35 (2000).

  13. 13.

    B. Islomov and U. I. Baltaeva, “Boundary-value problems for a third-order loaded parabolic-hyperbolic equation with variable coefficients,” Electron. J. Different. Equat., 2015, 1–10 (2015).

  14. 14.

    U. I. Baltaeva, “Solvability of the analogs of the problem Tricomi for the mixed type loaded equations with parabolic-hyperbolic operators,” Bound. Value Probl., 211, 1–12 (2014).

  15. 15.

    V. A. Vodakhova, R. G. Tlupova, and M. Kh. Shermetova, “Internally boundary-value problem for a loaded equation of the third order with multiple characteristics,” Usp. Sovrem. Estestvoznan., No. 1, 71–75 (2015).

  16. 16.

    T. D. Dzhuraev, A. Sopuev, and M. Mamazhonov, Boundary-Value Problems for the Equations of Parabolic-Hyperbolic Type [in Russian], Fan, Tashkent (1986).

  17. 17.

    A. S. Berdyshev, “On the basis property of root functions of one nonlocal problem for equations of the third order with parabolic-hyperbolic operator,” Differents. Uravn., 36, No. 3, 372–376 (2000).

  18. 18.

    D. Bazarov, “On an analog of the Bitsadze–Samarskii problem for a parabolic-hyperbolic equation of the third order,” Differents. Uravn., 25, No. 1, 21–27 (1989).

  19. 19.

    K. U. Khubiev, “One problem for a loaded equation of mixed hyperbolic-parabolic type,” Dokl. Adyg. Mezhdunar. Akad. Nauk, 7, No. 2, 74–77 (2005).

  20. 20.

    B. Islomov and U. I. Baltaeva, “Boundary-value problem with generalized gluing conditions for a loaded differential equation with parabolic-hyperbolic operator,” Vestn. KRAUNTS, Fiz.-Mat. Nauki, No. 3(14), 14–22 (2016).

  21. 21.

    K. B. Sabitov, “Constructions of solutions of the Darboux problems in the explicit form for the telegraph equation and their application to the inversion of integral equations. I,” Differents. Uravn., 26, No. 6, 1023–1032 (1990).

  22. 22.

    I. L. Krasnov, Integral Equations [in Russian], Nauka, Moscow (1976).

  23. 23.

    B. E. Eshmatov and E. T. Karimov, “Boundary-value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations,” Centr. Europ. J. Math., 5, No. 4, 741–750 (2007).

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Correspondence to U. I. Baltaeva.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 12, pp. 1587–1595, December, 2017.

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Baltaeva, U.I. On the Solvability of Boundary-Value Problems with Continuous and Generalized Gluing Conditions for the Equation of Mixed Type with Loaded Term. Ukr Math J 69, 1845–1854 (2018). https://doi.org/10.1007/s11253-018-1474-3

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