Geodesic
A~justification of the averaging method for a~problem of convection in a~field of rapidly oscillating forces and for other parabolic equations
Sbornik. Mathematics, Tome 16 (1972) no. 2, pp. 245-263

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Results of a previous paper of the author (Mat. Sb. (N.S.) 81(123) (1970), 53–61) are applied to parabolic equations and the Navier–Stokes equation. Of central importance is an investigation of the equation of convection in a vibrating container, which justifies the already completed formal application of the averaging method to deduce the stabilizing influence of a vibration (cf. S. M. Zen'kovskaya and I. V. Simonenko, On the influence of a high frequency vibration on the origin of convection, Izv. Akad. Nauk SSSR Ser. Meh. Zhidk. Gaza, 5 (1966), 51–55; S. M. Zen'kovskaya, An analysis of convection in a layer of fluid with the presence of a vibrational force, ibid. 1 (1968), 55–58). Bibliography: 16 titles. 
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     title = {A~justification of the averaging method for a~problem of convection in a~field of rapidly oscillating forces and for other parabolic equations},
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I. B. Simonenko. A~justification of the averaging method for a~problem of convection in a~field of rapidly oscillating forces and for other parabolic equations. Sbornik. Mathematics, Tome 16 (1972) no. 2, pp. 245-263. http://geodesic.mathdoc.fr/item/SM_1972_16_2_a7/