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Sib. Zh. Ind. Mat., 2018, Volume 21, Number 3, Pages 3–17 (Mi sjim1006)  

This article is cited in 1 scientific paper (total in 1 paper)

Properties of solutions for the problem of a joint slow motion of a liquid and a binary mixture in a two-dimensional channel

V. K. Andreevab, M. V. Efimovaab

a Institute of Computational Modeling, Akademgorodok 50/44, Krasnoyarsk, 660036 Russia
b Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660036 Russia

Abstract: Under study is a conjugate boundary value problemdescribing a joint motion of a binary mixture and a viscous heat-conducting liquid in a two-dimensional channel, where the horizontal component of the velocity vector depends linearly on one of the coordinates. The problemis nonlinear and inverse because the systems of equations contain the unknown time functions – the pressure gradients in the layers. In the case of small Marangoni numbers (the so-called creeping flow) the problem becomes linear. For its solutions the two different integral identities are valid which allow us to obtain a priori estimates of the solution in the uniform metric. It is proved that if the temperature on the channel walls stabilizes with time then, as time increases, the solution of the nonstationary problem tends to a stationary solution by an exponential law.

Keywords: conjugate problem, inverse problem, a priori estimates, surface tension, thermocapillarity, asymptotic behavior.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00229
The authors were supported by the Russian Foundation for Basic Research (project no. 17-01-00229).


DOI: https://doi.org/10.17377/sibjim.2018.21.301

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:3, 395–408

UDC: 517.9
Received: 12.02.2018
Revised: 13.06.2018

Citation: V. K. Andreev, M. V. Efimova, “Properties of solutions for the problem of a joint slow motion of a liquid and a binary mixture in a two-dimensional channel”, Sib. Zh. Ind. Mat., 21:3 (2018), 3–17; J. Appl. Industr. Math., 12:3 (2018), 395–408

Citation in format AMSBIB
\Bibitem{AndEfi18}
\by V.~K.~Andreev, M.~V.~Efimova
\paper Properties of solutions for the problem of a~joint slow motion of a~liquid and a~binary mixture in a~two-dimensional channel
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 3
\pages 3--17
\mathnet{http://mi.mathnet.ru/sjim1006}
\crossref{https://doi.org/10.17377/sibjim.2018.21.301}
\elib{https://elibrary.ru/item.asp?id=32872877}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 3
\pages 395--408
\crossref{https://doi.org/10.1134/S1990478918030018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052144719}


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    This publication is cited in the following articles:
    1. V. K. Andreev, I. V. Stepanova, “On the conditions for existence of unidirectional motions of binary mixtures in the Oberbeck–Boussinesq model”, J. Appl. Industr. Math., 13:2 (2019), 185–193  mathnet  crossref  crossref  elib
  • Сибирский журнал индустриальной математики
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