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 Mat. Sb. (N.S.), 1973, Volume 92(134), Number 4(12), Pages 541–549 (Mi msb3430)

Higher approximations of the averaging method for abstract parabolic equations

I. B. Simonenko

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.

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English version:
Mathematics of the USSR-Sbornik, 1973, 21:4, 535–543

Bibliographic databases:

UDC: 517.43+517.948+513.881
MSC: Primary 35K99, 35A35; Secondary 35Q10, 34C30

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/msb3430} \mathscinet{http://www.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 articles:
1. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “$G$-convergence of parabolic operators”, Russian Math. Surveys, 36:1 (1981), 9–60
2. V. B. Levenshtam, “Asymptotic expansion of the solution to the problem of vibrational convection”, Comput. Math. Math. Phys., 40:9 (2000), 1357–1365
3. V. B. Levenshtam, “Asymptotic integration of quasilinear parabolic equations with coefficients that rapidly oscillate with respect to time”, Russian Math. (Iz. VUZ), 46:5 (2002), 34–41
4. V. B. Levenshtam, “Construction of higher approximations of the averaging method for parabolic initial-boundary value problems by the boundary layer method”, Russian Math. (Iz. VUZ), 48:3 (2004), 37–41
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