Geodesic
On correctness of nonlocal edge problem with constant coefficient for multidimensional second order equation of mixed type
Matematičeskie zametki SVFU, Tome 24 (2017), pp. 17-27.

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We formulate a nonlocal boundary-value problem for a second order multidimensional equation of mixed type covering classical elliptic, hyperbolic, and parabolic equations. We prove regular solvability of the posed nonlocal boundary-value problem in Sobolev spaces.
Keywords: second order multidimensional equation of mixed type, nonlocal boundary value problem, generalized solution, regular solution, uniqueness, smoothness of solution, method of $\varepsilon$-regularization, Galerkin method, a priori estimates.
Mots-clés : existence 
@article{SVFU_2017_24_a1,
     author = {S. Z. Djamalov},
     title = {On correctness of nonlocal edge problem with constant coefficient for multidimensional second order equation of mixed type},
     journal = {Matemati\v{c}eskie zametki SVFU},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/SVFU_2017_24_a1/}
}
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S. Z. Djamalov. On correctness of nonlocal edge problem with constant coefficient for multidimensional second order equation of mixed type. Matematičeskie zametki SVFU, Tome 24 (2017), pp. 17-27. http://geodesic.mathdoc.fr/item/SVFU_2017_24_a1/

[1] Bitsadze A. V., Samarskii A. A., “About some protozoa generalizations of linear elliptic boundary-value problems”, Dokl. Akad. Nauk SSSR, 185:4 (1969), 739–740 | Zbl

[2] Vragov V. N., Boundary Value Problems for Nonclassical Equations of Mathematical Physics, Novosibirsk, Novosib. Gos. Univ., 1983 | MR

[3] Vragov V. N., “On the statement and solvability of boundary value problems for equations of mixed-composite type”, Mathematical Analysis and Related Questions of Mathematics, Inst. Mat. SO AN SSSR, Novosibirsk, 1978, 5–13

[4] Kozhanov A. I., Boundary Value Problems for Equations Mathematical Physics of Odd Order, Novosib. Gos. Univ., Novosibirsk, 1990 | MR

[5] Egorov I. E., Fedorov V. E., Higher-Order Nonclassical Equations of Mathematical Physics, Vychislit. Tsentr SO RAN, Novosibirsk, 1995 | MR

[6] Terekhov A. N., “Nonlocal boundary value problems for equations of the variable type”, Nonclassical Equations of Mathematical Physics, Inst. Mat. SO AN SSSR, Novosibirsk, 1985, 148–158

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

[8] Jamalov S. Z., “On the correctness of non-local boundary problems for a multidimensional equation of mixed type”, Application of Methods of Functional Analysis to Nonclassical Equations of Mathematical Physics, 1989, 63–70, Inst. Mat. SO AN SSSR, Novosibirsk | MR

[9] Karatopraklieva M. G., “On a nonlocal edge problem for a mixed-type equation”, Differ. Equ., 27:1 (1991), 68–79 | MR | Zbl

[10] Jamalov S. Z., “On a nonlocal boundary-value problem for an equation of mixed type of the second kind of second order”, Uzbek. Mat. Zhurn., 1:1 (2014), 5–14 | MR

[11] Kuzmin A. G., Nonclassical Equations of Mixed Type and Their Applications to Gas Dynamics, Leningr. Gos. Univ., Leningrad, 1990 | MR

[12] Berezanskiy Yu. M., Expansion by Eigenfunctions of Selfadjoint Operators, Naukova Dumka, Kiev, 1965 | MR

[13] Ladyzhenskaya O. A., Boundary-Value Problems of Mathematical Physics, Nauka, Moscow, 1973 | MR