Nonlocal problems with an integrally-disturbed A. A. Samarskii condition for third order quasi-parabolic equations
https://doi.org/10.25587/2411-9326-2023-4-12-23
Abstract
We study the solvability in anisotropic Sobolev spaces of nonlocal boundary problems for the third order quasi-parabolic equations with an integrally-disturbed Samarskii condition. A uniqueness and existence theorem is proved for regular solutions (i. e. the solutions that have all generalized derivatives that were used in equation).
About the Authors
A. I. Kozhanov
Sobolev Institute of Mathematics
Russian Federation
Russian Federation
Aleksandr I. Kozhanov
4 Koptyug Avenue, 630090 Novosibirsk
Д. Хромченко
Novosibirsk State University
Russian Federation
Russian Federation
Dmitrii S. Khromchenko
1 Pirogov Street, 630090 Novosibirsk
References
1. Ionkin N. I., “Solution of a boundary value problem of heat conduction theory with a non-classical boundary condition,” Differents. Uravn., 13, No. 2, 294–304 (1977).
2. Samarskij A. A., “On some problems of the theory of differential equations,”. Differents. Uravn., 16, No. 11, 1925–1935 (1980).
3. Ionkin N. I., “On the stability of a problem in the theory of heat conduction with a nonlocal boundary condition,” Differents. Uravn., 15, No. 7, 1279–1283 (1979).
4. Ionkin N. I. and Moiseev E. I., “On the problem for the heat equation with two-point boundary conditions,” Differents. Uravn., 15, No. 7, 1284–1295 (1979).
5. Yurchuk N. I., “Mixed problem with integral condition for some parabolic equations,” Differents. Uravn., 22, No. 12, 2117–2126 (1986).
6. Beilin S. A., “Existence of solutions for one-dimensional wave equations with nonlocal conditions,” Electron. J. Differ. Equ., 2001, No. 76, 1–8 (2001).
7. Berdyshev A. S., Cabada A., and Kadizkulov B. J., “The Samarskii–Ionkin type problem for the fourth order parabolic equation with fractional differential operator,” Comput. Math. Appl., 62, No. 10, 3884–3893 (2011).
8. Kozhanov A. I. and Abdrahmanov A. M., “Spatially nonlocal boundary value problems with the generalized Samarskii–Ionkin condition for quasi-parabolic equations,” Sib. Elektron. Mat. Izv., 20, No. 1, 110–123 (2023).
9. Sobolev S. L., Some Applications of Functional Analysis in Mathematical Physics, Nauka, Moscow (1988).
10. Ladyzjenskaya O. A. and Ural’tseva N. N., Linear and Quasilinear Equations of Elliptic Type, Nauka, Moscow (1964).
11. Triebel H., Interpolation Theory, Functional Spaces, Differential Operators, VEB Deutsch. Verl. Wiss., Berlin (1978).
12. Kozhanov A. I., “Initial-boundary value problems with a generalized Samarskii–Ionkin condition for parabolic equations with arbitrary evolution direction,” J. Math. Sci., 274, No. 2, 228–240 (2023).
13. Trenogin V. A., Functional Analysis, Nauka, Moscow (1980).
14. Kozhanov A. I., “Nonlocal problems with a generalized Samarskii–Ionkin condition for some classes of nonstationary differential equations,” Dokl. Akad. Nauk, 509, 50–53 (2023).
Review
For citations:
Kozhanov A.I., Nonlocal problems with an integrally-disturbed A. A. Samarskii condition for third order quasi-parabolic equations. Mathematical notes of NEFU. 2023;30(4):12-23. (In Russ.) https://doi.org/10.25587/2411-9326-2023-4-12-23
Views:
6
JATS XML
Email this article 