Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Aldashev S. A. Well-posedness of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 1, pp. 5-10. DOI: 10.18500/1816-9791-2014-14-1-5-10, EDN: SCSSPX

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.03.2014
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.956
DOI: 
10.18500/1816-9791-2014-14-1-5-10
EDN: 
SCSSPX

Well-posedness of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equation

Autors: 
Aldashev Serik Aimurzaevich, Abai Kazakh National Pedagogical University
Abstract: 

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

Key words: 
equation
problem
domain
function
References: 
  1. Fikera G. K edinoi teorii kraevykh zadach dlia elliptiko-parabolicheskikh uravnenii vtorogo poriadka [The unified theory of boundary value problems for elliptic-parabolic equations of second order]. Sbornik perevodov. Matematika. 1963, vol. 7, no. 6, pp. 99–121 (in Russian).
  2. Oleinik O. A., Radkevich E. V. Uravneniia s neotritsatel’noi kharakteristicheskoi formoi [Equations with nonnegative characteristic form]. Moscow, Moscow Univ. Press, 2010, 360 p. (in Russian).
  3. Mihlin S. G. Mnogomernye singulyarnye integraly i integral’nye uravneniya [Higher-dimensional singular integrals and integral equations]. Moscow, Gosudarstv. Izdat. Fiz.-Mat. Lit., 1962, 254 p. (in Russian).
  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. New York, Dover Publications, Inc., 1990. 765 p.
  5. Kamke E. Spravochnik po obyknovennym differentsial’nym [Manual of ordinary differential equations]. Third revised edition. Translated from the German by S. V. Fomin. Moscow, Nauka, 1965, 703 p. (in Russian).
  6. Beitmen G., Erdeii A. Vysshie transtsendentnyefunktsii. T. II: Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonal’nye mnogochleny [Higher transcendental functions. Vol. II: Bessel functions, parabolic cylinder functions, orthogonal polynomials]. Translated from the English by N. Ja. Vilenkin. Second edition, unrevised. Spravochnaya Matematicheskaya Biblioteka [Mathematical Reference Library]. Moscow, Nauka, 1974. 295 p. (in Russian).
  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., 2012, vol. 12, iss. 1, pp. 7–13 (in Russian).
  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., 2012, vol. 12, iss. 3, pp. 3–7 (in Russian).
Received: 
25.08.2013
Accepted: 
17.01.2014
Published: 
28.02.2014
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