Geodesic
A nonlocal boundary value problem with constant coefficients for the multidimensional second order equation of mixed type of the second kind
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 4, pp. 472-481.

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Multidimensional second order equation of the mixed type of the second kind is considered in the paper. Unique solvability and smoothness of the solution of a nonlocal boundary value problem with constant coefficients in Sobolev spaces are proved under some conditions on coefficients.
Keywords: solvability, generalized solution.
Mots-clés : multidimensional equations 
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Sirojiddin Z. Dzhamalov. A nonlocal boundary value problem with constant coefficients for the multidimensional second order equation of mixed type of the second kind. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 4, pp. 472-481. http://geodesic.mathdoc.fr/item/JSFU_2018_11_4_a8/

[1] V.N. Vragov, Boundary problems for non-classical equations of mathematical physics, Novosibirsk, 1983 (in Russian) | MR

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

[3] A.G. Kuzmin, Non-classical mixed type equations and their applications to the gas dynamics, Leningrad, 1990 (in Russian) | MR

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

[5] 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, Novosibirsk, 1983, 237–239 (in Russian) | MR

[6] S.Z. Dzhamalov, “On a nonlocal boundary value problem for a second order equation of mixed type of the second kind”, Uzbek. Math. J., 2014, no. 1, 5–14 (in Russian) | MR

[7] A.N. Terekhov, “Nonlocal boundary problems for equations of variable type”, Non-classical equations of mathematical physics, Novosibirsk, 1985, 148–158 (in Russian)

[8] 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

[9] S.Z. Dzhamalov, “On nonlocal boundary value problem with constant coefficients for the equation of Trikomi”, Uzbek. Mat. Zh., 2016, no. 2, 51–60 (in Russian) | MR

[10] O.A. Ladyjenskaya, Boundary problems of mathematical physics, Moscow, 1973 (in Russian) | MR

[11] Yu.M. Berezansky, Expansion in eigenfunctions of selfadjoint operators, Kyev, 1965 (in Russian)

[12] T.S. Kalmenov, “About a floor to a periodic problem for the multidimensional equation mixed type”, Differens. Uravn., 14:3 (1978), 546–548 (in Russian)

[13] A.I. Kozhanov, Boundary problems for equations of mathematical physics of odd order, Novosibirsk, 1990 (in Russian) | MR

[14] K.B. Sabitov, “Dirichlet problem for mixed type equations in rectangular domain”, Dokl. Math. RAN, 75:2 (2007), 193–196 | DOI | MR | Zbl

[15] B.N. Tsibikov, “About a correctness of a periodic problem for the multidimensional equation mixed type”, Non-classical equations of mathematical physics, 1986, 201–206 (in Russian) | MR