Geodesic
Higher approximations of the averaging method for abstract parabolic equations
Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 535-543 
I. B. Simonenko. Higher approximations of the averaging method for abstract parabolic equations. Sbornik. Mathematics, Tome 21 (1973) no. 4, pp. 535-543. http://geodesic.mathdoc.fr/item/SM_1973_21_4_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] I. B. Simonenko, “Obosnovanie metoda osredneniya dlya abstraktnykh parabolicheskikh uravnenii”, Matem. sb., 81 (123) (1970), 53–61 | MR | Zbl

[2] I. B. Simonenko, “Obosnovanie metoda osredneniya dlya zadachi konvektsii v pole bystro ostsilliruyuschikh sil i dlya drugikh parabolicheskikh uravnenii”, Matem. sb., 87 (129) (1972), 236–253 | MR | Zbl

[3] N. N. Bogolyubov, Yu. A. Mitropolskii, Asimptoticheskie metody v teorii nelineinykh kolebanii, Gostekhizdat, Moskva, 1955 | MR

[4] I. Z. Shtokalo, Lineinye differentsialnye uravneniya s peremennymi koeffitsientami, izd-vo AN USSR, Moskva, 1960

[5] M. A. Krasnoselskii, V. Sh. Burd, Yu. S. Kolesov, Nelineinye pochti periodicheskie kolebaniya, izd-vo «Nauka», Moskva, 1970 | MR

[6] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, P. E. Sobolevskii, Integralnye operatory v prostranstvakh summiruemykh funktsii, izd-vo «Nauka», Moskva, 1966 | MR

[7] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovykh prostranstvakh, izd-vo «Nauka», Moskva, 1967 | MR