Abstract
In the paper have been proved two theorems an averaging of convection problem and on stability or instability its periodic solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N.N. Bogoljubov, Yu.A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations. Nauka, Moscow, 1974 (in Russian).
B. Van der Pol, A theory of the amplitude of free and forced triode vibrations. The Radio Review. London 1 (1920), 701–710.
N.M. Krylov, N.N. Bogoljubov, Introduction to Nonlinear Mechanics. Izdatelstvo AN Ukr. SSR, Kiev (1937) (in Russian).
N.N. Bogoljubov, On Some Statistical Methods in Mathematical Physics. Izdatelstvo AN Ukr. SSR, Kiev (1945) (in Russian).
S.M. Zen’kovskaja, I.B. Simonenko, On the influence of a high-frequency vibration. on appearance of convection. Izvestiya AN SSSR. Mechanics of Fluids and Gas, No. 5 (1966) (in Russian).
S.M. Zen’kovskaja, On convection in a fluid layer under oblique vibrations, VINITI, No. 2437-78 (1978) (in Russian).
G.Z. Gershuni, E.M. Zhuhovitsky, On free heat convection in oscillating field under the conditions of weightlessness, Soviet Doklady 249 (1979), No. 3.
G.Z. Gershuni, E.M. Zhuhovitsky, On convective fluid instability in oscillating field, Izvestiya AN SSSR. Mechanics of Fluids and Gas, No. 4 (1981) (in Russian).
I.B. Simonenko, On the averaging method for the problem of convection in the high-frequency field of oscillating force, and some other parabolic equations, Mat. Sbornik 87 (1972), No. 2.
V.B. Levenshtam, On the averaging methods for the convection problem under high-frequency vibrations, Siberian Mat. Journ. 34 (1993), No. 2.
V.B. Levenshtam, On the averaging method for the problem of heat vibrational convection, Russian Doklady 349 (1996), No. 5.
V.B. Levenshtam, On the averaging method in the convection problem under high-frequency oblique vibrations, Siberian Mat. Journ. 37 (1996), No. 5.
V. Yudovich, The Linearization Method in Hydrodynamical Stability Theory, Transl. Math. Monographs. No. 74, Amer. Math. Soc., Providence (1989).
M.Z. Solomyak, Application of the semigroup theory to a study of differential equations in the Banach spaces, Soviet Doklady 125 (1958), No. 5.
P.E. Sobolevsky, Study of the Navier-Stokes equations by methods of the theory of parabolic equations in the Banach spaces, Soviet Doklady 156 (1964), No. 4.
P.E. Sobolevsky, On a coercive inequality for abstract parabolic equations, Soviet Doklady 157 (1964), No. 1.
M.A. Krasnoselsky, P.P. Zabreiko, E.I. Pustil’nik, P.E. Sobolevsky, Integral Operators in the Spaces of Integrable Functions. Nauka, Moscow, 1966 (in Russian).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to the 70th birthday of Professor I.B. Simonenko
Rights and permissions
Copyright information
© 2006 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Levenshtam, V.B. (2006). On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces. In: Erusalimsky, Y.M., Gohberg, I., Grudsky, S.M., Rabinovich, V., Vasilevski, N. (eds) Modern Operator Theory and Applications. Operator Theory: Advances and Applications, vol 170. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7737-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7737-3_11
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7736-6
Online ISBN: 978-3-7643-7737-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)