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Mathematics of the USSR-Sbornik, 1977, Volume 33, Issue 4, Pages 465–484
DOI: https://doi.org/10.1070/SM1977v033n04ABEH002434 (Mi sm2964) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On the stability of stationary solutions of nonlinear parabolic systems

V. S. Belonosov, M. P. Vishnevskii
English version PDF (1443 kB) Citations (11)
References:
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DOI: https://doi.org/10.1070/SM1977v033n04ABEH002434
Abstract: In this paper the linearization method is developed for the problem of stability of stationary solutions of nonlinear autonomous parabolic systems of general form. Estimates, uniform with respect to time, are established for Hölder norms of the solutions of the linearized systems. These estimates are then used in the study of the nonlinear problems. Theorems are proved concerning the stability of the first approximation and the conditional stability, generalizing the well-known Lyapunov theorems from the theory of ordinary differential equations.
Bibliography: 11 titles.
Received: 13.06.1977
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1977, Volume 104(146), Number 4(12), Pages 535–558
Bibliographic databases:
UDC: 517.946
MSC: Primary 35B35, 35K55; Secondary 35B45
Language: English
Original paper language: Russian
Citation: V. S. Belonosov, M. P. Vishnevskii, “On the stability of stationary solutions of nonlinear parabolic systems”, Mat. Sb. (N.S.), 104(146):4(12) (1977), 535–558; Math. USSR-Sb., 33:4 (1977), 465–484
Citation in format AMSBIB
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\by V.~S.~Belonosov, M.~P.~Vishnevskii
\paper On~the stability of stationary solutions of nonlinear parabolic systems
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 104(146)
\issue 4(12)
\pages 535--558
\mathnet{http://mi.mathnet.ru/sm2964}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=499728}
\zmath{https://zbmath.org/?q=an:0448.35014}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 33
\issue 4
\pages 465--484
\crossref{https://doi.org/10.1070/SM1977v033n04ABEH002434}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1977GX43200002}
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  • https://doi.org/10.1070/SM1977v033n04ABEH002434
  • https://www.mathnet.ru/eng/sm/v146/i4/p535
    • This publication is cited in the following 11 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:945
    Russian version PDF:238
    English version PDF:6
    References:45
     
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