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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 6, Pages 1045–1057 (Mi zvmmf458)  

This article is cited in 2 scientific papers (total in 2 papers)

Approximate method for solving the boundary value problem for a parabolic equation with inhomogeneous transmission conditions of nonideal contact type

D. A. Nomirovskii

Faculty of Cybernetics, National University of Kiev, pr. Glushkova 6, Kiev, 03022, Ukraine

Abstract: A linear parabolic equation in a disconnected domain with inhomogeneous transmission conditions of the nonideal contact type is studied. A generalized formulation of the problem is considered. An analogue of the Galerkin method is proposed for solving the problem, and the stability of the method is investigated. This makes it possible to prove existence and uniqueness theorems for the equation under different assumptions on the data smoothness.

Key words: parabolic equation, Galerkin method, transmission conditions, nonideal contact, solvability, generalized functions.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:6, 995–1006

Bibliographic databases:

UDC: 519.633
Received: 26.01.2004
Revised: 13.12.2005

Citation: D. A. Nomirovskii, “Approximate method for solving the boundary value problem for a parabolic equation with inhomogeneous transmission conditions of nonideal contact type”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 1045–1057; Comput. Math. Math. Phys., 46:6 (2006), 995–1006

Citation in format AMSBIB
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\by D.~A.~Nomirovskii
\paper Approximate method for solving the boundary value problem for a~parabolic equation with inhomogeneous transmission conditions of nonideal contact type
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 6
\pages 1045--1057
\mathnet{http://mi.mathnet.ru/zvmmf458}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2285364}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 6
\pages 995--1006
\crossref{https://doi.org/10.1134/S096554250606008X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746179113}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nomirovskii D., “Generalized solvability and optimization of a parabolic system with a discontinuous solution”, J. Differential Equations, 233:1 (2007), 1–21  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Nomirovskii D.A., Vostrikov O.I., “Generalized Statements and Properties of Models of Transport Processes in Domains with Cuts”, Cybern. Syst. Anal., 52:6 (2016), 931–942  crossref  mathscinet  zmath  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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