This article is cited in 5 papers

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.

UDC: 517.43+517.948+513.881

MSC: Primary 35K99, 35A35; Secondary 35Q10, 34C30

Received: 18.12.1972

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

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