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Mathematics of the USSR-Sbornik, 1973, Volume 21, Issue 4, Pages 535–543
DOI: https://doi.org/10.1070/SM1973v021n04ABEH002034 (Mi sm3430) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Higher approximations of the averaging method for abstract parabolic equations

I. B. Simonenko
English version PDF (461 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM1973v021n04ABEH002034
Abstract: In the authors's article in this journal, vol. 81(123) (1970), pp. 53–61, it was shown that the averaging method of N. N. Bogolyubov can be applied to abstract parabolic equations with unbounded operators which generate analytic semigroups. The nearness of the solutions of the original and the averaged equations in a certain norm was proved.
In the present article it is shown that the successive approximations of the averaging method are near the solution of the original equation in stronger norms and in a stronger asymptotic sense.
Bibliography: 7 titles.
Received: 18.12.1972
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1973, Volume 92(134), Number 4(12), Pages 541–549
Bibliographic databases:
UDC: 517.43+517.948+513.881
MSC: Primary 35K99, 35A35; Secondary 35Q10, 34C30
Language: English
Original paper language: Russian
Citation: I. B. Simonenko, “Higher approximations of the averaging method for abstract parabolic equations”, Mat. Sb. (N.S.), 92(134):4(12) (1973), 541–549; Math. USSR-Sb., 21:4 (1973), 535–543
Citation in format AMSBIB
\Bibitem{Sim73}
\by I.~B.~Simonenko
\paper Higher approximations of the averaging method for abstract parabolic equations
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 92(134)
\issue 4(12)
\pages 541--549
\mathnet{http://mi.mathnet.ru/sm3430}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=340755}
\zmath{https://zbmath.org/?q=an:0303.35004}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 21
\issue 4
\pages 535--543
\crossref{https://doi.org/10.1070/SM1973v021n04ABEH002034}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:271
    Russian version PDF:111
    English version PDF:7
    References:39
     
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