The nonlocal boundary value problem with constant coefficients for the mixed-type equation of the second kind and of the second order in a rectangle
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 4, pp. 12-22.

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In the present work for the second order mixed-type equation of the second kind we study one-valued solvability and smoothness of the generalized solution of nonlocal boundary value problem with constant coefficients in Sobolev spaces.
Keywords: second order mixed type equation of the second kind, nonlocal boundary value problem with constant coefficients, uniqueness, existence and smoothness of generalized solution, Sobolev space, Galerkin method, "$\varepsilon$-regularization" method.
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S. Z. Djamalov. The nonlocal boundary value problem with constant coefficients for the mixed-type equation of the second kind and of the second order in a rectangle. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 4, pp. 12-22. http://geodesic.mathdoc.fr/item/SVMO_2017_19_4_a0/

[1] N. A. Alimov, “On a nonlocal boundary value problem for a non-classical equation”, The theory and methods for solving ill-posed problems and their applications, NGU, Novosibirsk, 1983, 237–239 (In Russ)

[2] Yu . M. Berezansky, Expansion in eigenfunctions of selfadjoint operators, Naukova dumka, Kyev, 1965, 798 pp. (In Russ) | MR

[3] V . N. Vragov, Boundary problems for non-classical equations of mathematical physics, NGU, Novosibirsk, 1983, 84 pp. (In Russ) | MR

[4] S. N. Glazatov, “Nonlocal boundary problems for mixed type equations in a rectangle”, Siberian Math. Journ, 26:6 (1985), 162–164 (In Russ) | MR

[5] S. Z. Dzhamalov, “About one nonlocal boundary value problem for the equation of the mixed type of the second kind of the second order”, Uzbek mathematical journal, 2014, no. 1, 5–14 (In Russ) | MR

[6] S. Z. Dzhamalov, “The nonlocal boundary value problem with constant coefficients for the equation of Trikomi”, Uzbek mathematical journal, 2016, no. 2, 51–60 (In Russ) | MR

[7] S. Z. Djamalov, “On the correctness of a nonlocal problem for the second order mixed type equations of the second kind in a rectangle”, IIUM journal, 17:2 (2016), 95–104 | DOI

[8] M. G. Karatopraklieva, “A nonlocal boundary-value problem for an equation of mixed type”, Differents. uravneniy, 27:1 (1991), 68–79 (In Russ) | MR | Zbl

[9] A. I. Kozhanov, Boundary problems for equations of mathematical physics of odd order, NGU, Novosibirsk, 1990, 130 pp. (In Russ) | MR

[10] A. G. Kuzmin, Non-classical mixed type equations and their applications to the gas dynamics, LGU, Leningrad, 1990, 204 pp. (In Russ) | MR

[11] O. A. Ladyjenskaya, Boundary problems of mathematical physics, Nauka, Moscow, 1973, 407 pp. (In Russ) | MR

[12] A. N. Terekhov, “Nonlocal boundary problems for equations of variable type”, Nonclassical equations of mathematical physics, NGU, Novosibirsk, 1985, 148–158 (In Russ)