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Mathematics of the USSR-Sbornik, 1977, Volume 33, Issue 4, Pages 519–537
DOI: https://doi.org/10.1070/SM1977v033n04ABEH002439 (Mi sm2983) 		 
This article is cited in 48 scientific papers (total in 48 papers)

On the stabilization of solutions of parabolic equations

V. V. Zhikov
English version PDF (1096 kB) Citations (48)
References:
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DOI: https://doi.org/10.1070/SM1977v033n04ABEH002439
Abstract: In this paper, a method for studying stabilization properties of second order, and also higher order, equations is presented. In particular, pointwise stabilization criteria are obtained for the equation $cu_t=\Delta u$, the only requirement on the coefficient $c(x)$ being the existence of a mean value. This result generalizes known results of Gushchin and Mihailov, as well as the corresponding results for the equation of heat conduction. Analogous criteria are developed for the equation $cu_t+(-1)^m\Delta^mu=0$. Stabilization criteria are proved for other equations as well.
Bibliography: 8 titles.
Received: 22.11.1976
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1977, Volume 104(146), Number 4(12), Pages 597–616
Bibliographic databases:
UDC: 517.946
MSC: Primary 35K15, 35B40; Secondary 35K30
Language: English
Original paper language: Russian
Citation: V. V. Zhikov, “On the stabilization of solutions of parabolic equations”, Mat. Sb. (N.S.), 104(146):4(12) (1977), 597–616; Math. USSR-Sb., 33:4 (1977), 519–537
Citation in format AMSBIB
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\by V.~V.~Zhikov
\paper On~the stabilization of solutions of parabolic equations
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 104(146)
\issue 4(12)
\pages 597--616
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=473524}
\zmath{https://zbmath.org/?q=an:0374.35025|0398.35048}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 33
\issue 4
\pages 519--537
\crossref{https://doi.org/10.1070/SM1977v033n04ABEH002439}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977GX43200005}
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  • https://doi.org/10.1070/SM1977v033n04ABEH002439
  • https://www.mathnet.ru/eng/sm/v146/i4/p597
    • This publication is cited in the following 48 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:706
    Russian version PDF:256
    English version PDF:32
    References:76
    First page:1
     
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