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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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

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

[3] S. M. Zenkovskaya, I. B. Simonenko, “O vliyanii vibratsii vysokoi chastoty na vozniknovenie konvektsii”, Mekhanika zhidkosti i gaza, no. 5, 1966, 51–55

[4] S. M. Zenkovskaya, “Issledovanie konvektsii v sloe zhidkosti pri nalichii vibratsionnykh sil”, Mekhanika zhidkosti i gaza, no. 1, 1968, 55–58

[5] S. M. Zenkovskaya, I. B. Simonenko, “Issledovanie vliyaniya vibratsii vysokoi chastoty na vozniknovenie konvektsii”, Tretii Vsesoyuznyi s'ezd po teoreticheskoi i prikladnoi mekhanike, Annotatsiya dokladov, Moskva, 1968, 137

[6] S. Agmon, “On the eigenfuctions and on the eigenvalues of general elleptic boundary value problems”, Comm. Pure and Appl. Math., 15:2 (1962), 119–158 | DOI | MR

[7] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, P. E. Sobolevskii, Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, Moskva, 1966 | MR

[8] M. Z. Solomyak, “Primenenie teorii polugrupp k issledovaniyu differentsialnykh uravnenii v prostranstvakh Banakha”, DAN SSSR, 122:5 (1958), 766–769

[9] K. Yosida, “Fractional powers of infinitesimal generators and the analyticity of the semigroups generated by them”, Proc. Japan Acad., 36 (1960), 86–89 | DOI | MR | Zbl

[10] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovykh prostranstvakh, Nauka, Moskva, 1967 | MR

[11] V. I. Yudovich, “Ob ustoichivosti statsionarnykh techenii vyazkoi neszhimaemoi zhidkosti”, DAN SSSR, 161:5 (1965), 1037–1040 | Zbl

[12] L. D. Landau, E. M. Lifshits, Mekhanika sploshnykh sred, Gostekhizdat, Moskva, 1953

[13] O. V. Besov, V. P. Ilin, L. D. Kudryavtsev, P. I. Lizorkin, S. M. Nikolskii, “Teoriya vlozhenii klassov differentsiruemykh funktsii mnogikh peremennykh”, Differentsialnye uravneniya s chastnymi proizvodnymi, Nauka, Moskva, 1970, 38–63 | MR

[14] V. A. Solonnikov, “Ob otsenkakh tenzora Grina dlya nekotorykh kraevykh zadach”, DAN SSSR, 130:5 (1960), 988–991 | MR | Zbl

[15] I. I.Vorovich, V. I. Yudovich, “Statsionarnoe techenie vyazkoi neszhivaemoi zhidkosti”, Matem. sb., 53(95) (1961), 393–427

[16] V. I. Yudovich, “Ob odnom proektore dinamiki vyazkoi neszhimaemoi zhidkosti”, Matem. analiz i ego primeneniya, t. III, IRU, Rostov-na-Donu, 1971, 31–36