Asymptotic expansion of the solution to the problem of vibrational convection

Computational Mathematics and Mathematical Physics

Volumn 40, Issue 9, 2000, Pages 1357-1365

  Levenshtam, V B ^a  

^a SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

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EID: 15844411478     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Levenshtam, V.B., Higher-Order Approximations of the Averaging Method for the Vibration Convection, Differ. Uravn., 1995, vol. 31, no. 5, pp. 814-822.
2. Levenshtam, V.B., Asymptotic Integration of the Vibration Convection Problem, Differ. Uravn., 1997, vol. 34, no. 4, pp. 523-532.
3. Bogolyubov, N.N. and Mitropol'skii, Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii (Asymptotic Methods in the Theory of Nonlinear Vibrations), Moscow: Nauka, 1974.
4. Simonenko, I.B., Higher-Order Approximations of the Averaging Method for Abstract Parabolic Equations, Mat. Sb., 1973, vol. 92(134), no. 4, pp. 541-549.
5. Vishik, M.I. and Lyusternik, L.A., Regular Degeneracy and the Boundary Layer for Nonlinear Differential Equations with a Small Parameter, Usp. Mat. Nauk, 1960, vol. 15, no. 4, pp. 3-95.
6. Ladyzhenskaya, O.A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti (Mathematical Issues of the Dynamics of Viscous Incompressible Liquid), Moscow: Nauka, 1970.
7. Levenshtam, V.B., Justification of the Averaging Method for the Problem of Heat Vibration Convection, Dokl. Ross. Akad. Nauk, 1996, vol. 349, no. 5, pp. 621-623.
8. Solonnikov, V.A., Differential Properties of Solutions to the First Boundary Value Problem for the Time-Dependent Navier-Stokes System of Equations, Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR, 1964, vol. 73, pp. 221-291.
9. Kochin, N.N., Kibel', I.A., and Roze, N.V., Teoreticheskaya gidromekhanika (Theoretical Hydromechanics), Moscow: Fizmatgiz, 1963, ch. II.
10. Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural'tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Parabolic Equations), Moscow: Nauka, 1967.
11. Yudovich, V.I., Metod linearizatsii v gidrodinamicheskoi teorii ustoichivosti (Linearization Method in Hydrodynamic Stability Theory), Rostov-on-Don: Rostov. Gos. Univ., 1984.
12. Levenshtam, V.B., Averaging Method for the Convection Problem under High-Frequency Vibrations, Sib. Mat. Zh., 1993, vol. 34, no. 2, pp. 92-109.