Solvability Dirichlet problem for three-dimensional elliptic-parabolic equations with type and order extinction

  • E. T. Kitaybekov Казахский национальный педагогический университет имени Абая, Республика Казахстан, г. Алматы


Correctness of boundary problems in the plane for elliptic equations is well analyzed by analitic function theory of complex variable. There appear principal difficulties in similar problems when the number of independent variables is more than two. An attractive and suitable method of singular integral equations is less strong because of lock of any complete theory of multidimensional singular integral equations. In the works of S.A. Aldasheva, shows the unique solvability and obtained form of the explicit Dirichlet problem in the cylindrical domain for multidimensional elliptic-parabolic equations. In this paper, for the three-dimensional elliptic-parabolic equations with degeneration of the type and order in a cylindrical domain shown solvability and obtained in the form of a classical solution of the Dirichlet problem.


[1] Fichera G. For a unified theory of boundary value problems for elliptic-parabolic equations of the second order // Coll. translations. Mathematics, 1963.- Vol. 7. No 6 -P. 99-121.
[2] Vragov V.N. Boundary value problems for nonclassical equations of Math Physics. -Novosibirsk: NSU, 1983.- 84 p.
[3] Aldashev S. A. The correctness of the Dirichlet problem for degenerate elliptic-dimensional parabolic equations // Journal of Computational and Applied Mathematics. -Kyiv, 2014. -No.3 (117) -P. 17-22.
[4] Aldashev S. A. The Dirichlet problem in a cylindrical domain for multidimensional degenerate elliptic-parabolic equations // Actual problems of the theory of partial differential equations: Abstracts Int. Conf. dedicated to the 100th anniversary of A. Bitsadze. -Moscow, 2016. - P. 14.
[5] Aldashev S. A. Correctness of Dirichlet problem for degenerating multi-dimensional hyperbolic-parabolic equations// Vladikavkaz math. journal. -2014. -Vol. 16, No.4. -P. 3-8.
[6] Kolmogorov A. N., Fomin S. V. Elements of function theory and functional analysis. –M.: Nauka, 1976. -543 с.
[7] Aldashev S. A., Kitaybekov E.T. The correctness Dirichlet problem in a cylindrical domain for three-dimensional elliptic equations with type and order extinction // Analysis and Applied Mathematics: Third Intern. Conf. on Institut of Mathematics and Mathematical Modelling. -Almaty: 2016. -P.30.
How to Cite
KITAYBEKOV, E. T.. Solvability Dirichlet problem for three-dimensional elliptic-parabolic equations with type and order extinction. KazNU Bulletin. Mathematics, Mechanics, Computer Science Series, [S.l.], v. 92, n. 4, p. 40-45, july 2018. ISSN 1563-0277. Available at: <>. Date accessed: 17 aug. 2018.
Keywords: solvability, Dirichlet problem, degeneration of the type and order, density