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Mathematics of the USSR-Sbornik, 1972, Volume 16, Issue 2, Pages 245–263
DOI: https://doi.org/10.1070/SM1972v016n02ABEH001424 (Mi sm3047) 		 
This article is cited in 48 scientific papers (total in 48 papers)

A justification of the averaging method for a problem of convection in a field of rapidly oscillating forces and for other parabolic equations

I. B. Simonenko
English version PDF (1004 kB) Citations (48) Russian version article
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DOI: https://doi.org/10.1070/SM1972v016n02ABEH001424
Abstract: Results of a previous paper of the author (Mat. Sb. (N.S.) 81(123) (1970), 53–61) are applied to parabolic equations and the Navier–Stokes equation. Of central importance is an investigation of the equation of convection in a vibrating container, which justifies the already completed formal application of the averaging method to deduce the stabilizing influence of a vibration (cf. S. M. Zen'kovskaya and I. V. Simonenko, On the influence of a high frequency vibration on the origin of convection, Izv. Akad. Nauk SSSR Ser. Meh. Zhidk. Gaza, 5 (1966), 51–55; S. M. Zen'kovskaya, An analysis of convection in a layer of fluid with the presence of a vibrational force, ibid. 1 (1968), 55–58).
Bibliography: 16 titles.
Received: 04.12.1970
Bibliographic databases:
UDC: 517.43+517.948+513.881
MSC: Primary 76D05, 35K25; Secondary 76D99
Language: English
Original paper language: Russian
Citation: I. B. Simonenko, “A justification of the averaging method for a problem of convection in a field of rapidly oscillating forces and for other parabolic equations”, Math. USSR-Sb., 16:2 (1972), 245–263
Citation in format AMSBIB
\Bibitem{Sim72}
\by I.~B.~Simonenko
\paper A~justification of the averaging method for a~problem of convection in a~field of rapidly oscillating forces and for other parabolic equations
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 2
\pages 245--263
\mathnet{http://mi.mathnet.ru/eng/sm3047}
\crossref{https://doi.org/10.1070/SM1972v016n02ABEH001424}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=295150}
\zmath{https://zbmath.org/?q=an:0253.35049}
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    • This publication is cited in the following 48 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
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