ON SMOOTHNESS OF THE SOLUTION TO A NONLOCAL BOUNDARY VALUE PROBLEM OF PERIODIC TYPE FOR A FOURTH-ORDER MIXED-TYPE EQUATION OF THE SECOND KIND
In this paper, using the modified Galerkin method and the methods of a priori
estimates, “"-regularization”, we study the unique solvability and smoothness of a
regular generalized solution of a nonlocal boundary value problem of periodic type
for a mixed type equation of the second kind of the fourth order in Sobolev spaces
1. Berezinsky Yu. M. Expansion in eigenfunctions of self-adjoint operators. Kyiv: Naukova
Dumka, (1965).
2. Bitsadze A. V. Ill-posedness of the Dirichlet problem for equations of mixed type // DAN
USSR. V.122, No. 4, 167–170 (1953).
3. Vragov V. N. Boundary value problems for non-classical equations of mathematical
physics. Novosibirsk: NSU, (1983).
4. Vragov V. N. On the formulation and solvability of boundary value problems for equations
of mixed-composite type // Mathematical analysis and related issues of mathematics.
Novosibirsk: IM SO AN USSR, 5–13 (1978).
5. Egorov I. E., Fedorov V. E. Nonclassical equations of high order mathematical physics.
Novosibirsk, 133 p. (1995).
6. Glazatov S. N. Nonlocal boundary value problems for equations of mixed type in a
rectangle // Sibirsk. Math. J., V. 26, No. 6, 162–164 (1985).
7. Dzhamalov S. Z. On the well-posedness of a nonlocal boundary value problem with
constant coefficients for a mixed type equation of the second kind of second order in
space // Math. NEFU notes, No. 4, 17–28 (2017).
8. Dzhamalov S. Z. On the smoothness of a nonlocal boundary value problem for a
multidimensional equation of mixed type of the second kind in space // Journal of the
Middle Volga Math Society, V. 21, No. 1, 24–33 (2019).
9. Dzhamalov S. Z. Nonlocal boundary value and inverse problems for equations of mixed
type. Monograph. Tashkent. 173 p.
10. Dzhamalov S. Z., Pyatkov S. G. On some classes of boundary value problems for multidimensional
equations of mixed type of high order // Siberian Mathematical Journal,
V. 61, No. 4, 777–795 (2020).
11. Dezin A. A. General questions of the theory of boundary value problems. - M: Nauka,
(1980).
12. Ladyzhenskaya O. A. Boundary value problems of mathematical physics. M. 407 p. (1973).
13. Frankl F. I. Selected works on gas dynamics: Moscow. 711 p. (1973) [in Russian].
14. Karatopraklieva M. G. On a nonlocal boundary value problem for an equation of mixed
type // Differential equations, V. 27, No. 1, 68–79 (1991).
15. Kozhanov A. I. Boundary value problems for equations of mathematical physics of odd
order // Novosibirsk: NSU, (1990).
16. Terekhov A. N. Nonlocal boundary value problems for equations of variable type.
Nonclassical equations of mathematical physics. Novosibirsk: IM SO AN USSR, 148–158
(1985).
17. Trenogin V. A. Functional analysis. Moscow. Nauka, 494 p. [in Russian].
18. Chueshev A. V. On one linear equation of mixed type of high order // Sibirsk. Math. J.,
V. 43, No. 2, 454–472 (2002).
19. Djuraev T. D., Sopuev A. K teorii differensial’nyx uravneniy v chastnyx proizvodnyx
chetvertogo poryadka. - Tashkent: Fan. - 144 s. (2000).
20. Sabitov K. B. Zadacha Dirixle dlya uravneniy smeshannogo tipa v pryamougol’noy oblasti
// Dokl. RAN. T.413. No. 1, 23–26 (2007).
Copyright (c) 2025 «ACTA NUUz»
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
.jpg)
1.png)
