Well-posedness of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 1, pp. 5-10
S. A. Aldashev. Well-posedness of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 1, pp. 5-10. http://geodesic.mathdoc.fr/item/ISU_2014_14_1_a0/
@article{ISU_2014_14_1_a0,
     author = {S. A. Aldashev},
     title = {Well-posedness of the {Dirichlet} problem in a~cylindrical domain for multidimensional elliptic-parabolic equation},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {5--10},
     year = {2014},
     volume = {14},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_1_a0/}
}
TY  - JOUR
AU  - S. A. Aldashev
TI  - Well-posedness of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equation
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2014
SP  - 5
EP  - 10
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2014_14_1_a0/
LA  - ru
ID  - ISU_2014_14_1_a0
ER  - 
%0 Journal Article
%A S. A. Aldashev
%T Well-posedness of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equation
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2014
%P 5-10
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2014_14_1_a0/
%G ru
%F ISU_2014_14_1_a0

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

A unique solvability of classic solutions to Dirichlet's problem in the cylindrical domain for the model multidimensional elliptic-parabolic equation is shown in the article.

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

[2] Oleinik O. A., Radkevich E. V., Equations with nonnegative characteristic form, Moscow Univ. Press, Moscow, 2010, 360 pp.

[3] Mihlin S. G., Higher-dimensional singular integrals and integral equations, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1962, 254 pp. | MR

[4] Tikhonov A. N., Samarskii A. A., Equations of mathematical physics, Translated from the Russian by A. R. M. Robson and P. Basu. Reprint of the 1963 translation, Dover Publications, Inc., New York, 1990, 765 pp. | MR

[5] Kamke E., Manual of ordinary differential equations, Translated from the German by S. V. Fomin, Third revised edition, Nauka, Moscow, 1965, 703 pp. | MR

[6] Beitmen G., Erdeii A., Higher transcendental functions, Translated from the English by N. Ja. Vilenkin, v. II, Mathematical Reference Library, Bessel functions, parabolic cylinder functions, orthogonal polynomials, Second edition, unrevised, Nauka, Moscow, 1974, 295 pp.

[7] Aldashev S. A., “The correctness of the Dirichlet problem in the cylindric domain for one class of multi-dimensional elliptic equations”, Vestnik, Quart. J. of Novosibirsk State Univ. Ser. Math., mech., inform., 12:1 (2012), 7–13 | Zbl

[8] Aldashev S. A., “The correctness of the Dirichlet problem in the cylindric domain for equation Laplase”, Izv. Saratov. Univ. (N.S.), Ser. Math. Mech. Inform., 12:3 (2012), 3–7