This article is cited in 48 papers

A justification of the averaging method for a problem of convection in a field of rapidly oscillating forces and for other parabolic equations

I. B. Simonenko


Abstract: 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.

UDC: 517.43+517.948+513.881

MSC: Primary 76D05, 35K25; Secondary 76D99

Received: 04.12.1970

 English version: Mathematics of the USSR-Sbornik, 1972, 16:2, 245–263

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