Geodesic
Well-posedness of the Dirichlet problem for a class of multidimensional elliptic-parabolic equations
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 125-132.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 work, the method proposed in the author’s works, shows the unique solvability and obtained the explicit form of the Dirichlet problem in the cylindric domain for a class of multidimensional elliptic-parabolic equations. 
@article{ISU_2016_16_2_a0,
     author = {S. A. Aldashev},
     title = {Well-posedness of the {Dirichlet} problem for a class of multidimensional elliptic-parabolic equations},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {125--132},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a0/}
}
TY  - JOUR
AU  - S. A. Aldashev
TI  - Well-posedness of the Dirichlet problem for a class of multidimensional elliptic-parabolic equations
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2016
SP  - 125
EP  - 132
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a0/
LA  - ru
ID  - ISU_2016_16_2_a0
ER  - 
%0 Journal Article
%A S. A. Aldashev
%T Well-posedness of the Dirichlet problem for a class of multidimensional elliptic-parabolic equations
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2016
%P 125-132
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a0/
%G ru
%F ISU_2016_16_2_a0
S. A. Aldashev. Well-posedness of the Dirichlet problem for a class of multidimensional elliptic-parabolic equations. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 125-132. http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a0/

[1] Fikera G., “The unified theory of boundary value problems for elltptlc-parabolic equations of second order”, Sbornik perevodov. Matematika, 7:6 (1963), 99–121 (in Russian)

[2] Oleinik O. A., Radkevich E. V., Equations with nonnegativo characteristic form, Moscow Univ. Press, M., 2010, 360 pp. (in Russian)

[3] Aldashev S. A., “The correctness of the Dirichlet problem in the cylindric domain for the multidimensional elliptic-parabolic equation”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:1 (2014), 5–10 (in Russian)

[4] Aldashev S. A., “Correctness of Dirichlet's Problem in a Cylindric Domain for a Single Class of Many-dimensional Elliptic Equations”, Vestn. Novosib. Gos. Univ., Ser. Matem., Mekh., Inform., 12:1 (2012), 7–13 (in Russian) | MR

[5] Mikhlin S. G., Multidimensional Singular Integrals and Integral Equations, Pergamon, New York, 1965 | MR | MR | Zbl

[6] Aldashev S. A., Boundary-Value Problems for Multi-Dimensional Hyperbolic and Mixed Equations, Gylym Press, Almaty, Kazakhstan, 1994, 170 pp. (in Russian)

[7] Aldashev S. A., “On Darboux problems for a class of multidimensional hyperbolic equations”, Differentsialnye Uravneniya, 34:1 (1998), 64–68 (in Russian) | MR

[8] Aldashev S. A., Degenerate multidimensional hyperbolic equation, ZKATU, Oral, 2007, 139 pp. (in Russian)

[9] Kamke E., Handbook on Ordinary Differential Equations, Nauka, M., 1965, 703 pp. (in Russian) | MR

[10] Beitmen G., Erdeii A., Higher Transcendental Functions, v. 2, Nauka, M., 1974, 297 pp. (in Russian)

[11] Kolmogorov A., Fomin S., Elements of the Theory of Functions and Functional Analysis, Dover Publications, Mineola, NY, USA, 1999 | MR

[12] Tikhonov A. N., Samarskii A. A., Equations of mathematical physics, Nauka, M., 1966, 724 pp. (in Russian) | MR

[13] Smirnov V. I., The higher mathematics course, pt. 2, v. 4, Nauka, M., 1981, 550 pp. (in Russian)

[14] Friedman A., Partial differential Equations of parabolic type, Mir, M., 1968, 527 pp. (in Russian)

[15] Bers L., John F., Schechter M., Partial differential equations, Mir, M., 1966, 352 pp. (in Russian) | MR