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Mathematics of the USSR-Sbornik, 1987, Volume 58, Issue 2, Pages 491–503
DOI: https://doi.org/10.1070/SM1987v058n02ABEH003116 (Mi sm1888) 		 
This article is cited in 29 scientific papers (total in 29 papers)

Bifurcation of self-oscillations of nonlinear parabolic equations with small diffusion

A. B. Vasil'eva, S. A. Kashchenko, Yu. S. Kolesov, N. Kh. Rozov
English version PDF (786 kB) Citations (29)
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DOI: https://doi.org/10.1070/SM1987v058n02ABEH003116
Abstract: First, the questions of existence, multiplicity, and stability of timeperiodic solutions of the van der Pol equations with small diffusion are considered. It is shown that in some situations, the principle of averaging for parabolic equations plays a significant role in justifying these results. In this connection, the justification of the principle is given. At the end of the paper, it is indicated that the results allow one to investigate the well-known problem of the existence of spatially nonhomogeneous regimes in homogeneous media.
Bibliography: 26 titles.
Received: 06.03.1984 and 04.02.1985
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1986, Volume 130(172), Number 4(8), Pages 488–499
Bibliographic databases:
UDC: 517.926
MSC: Primary 35K55; Secondary 35B10, 35B40
Language: English
Original paper language: Russian
Citation: A. B. Vasil'eva, S. A. Kashchenko, Yu. S. Kolesov, N. Kh. Rozov, “Bifurcation of self-oscillations of nonlinear parabolic equations with small diffusion”, Mat. Sb. (N.S.), 130(172):4(8) (1986), 488–499; Math. USSR-Sb., 58:2 (1987), 491–503
Citation in format AMSBIB
\Bibitem{VasKasKol86}
\by A.~B.~Vasil'eva, S.~A.~Kashchenko, Yu.~S.~Kolesov, N.~Kh.~Rozov
\paper Bifurcation of self-oscillations of nonlinear parabolic equations with small diffusion
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 130(172)
\issue 4(8)
\pages 488--499
\mathnet{http://mi.mathnet.ru/sm1888}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=867339}
\zmath{https://zbmath.org/?q=an:0637.35009}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 2
\pages 491--503
\crossref{https://doi.org/10.1070/SM1987v058n02ABEH003116}
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  • https://www.mathnet.ru/eng/sm/v172/i4/p488
    • This publication is cited in the following 29 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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    Abstract page:699
    Russian version PDF:207
    English version PDF:11
    References:44
    First page:2
     
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