The averaging method in the convection problem with high-frequency oblique vibrations
type: Item
instance of: scholarly article
title: The averaging method in the convection problem with high-frequency oblique vibrations
zbMATH Open document ID: 0874.35094
DOI: 10.1007/BF02110727
author: V. B. Levenshtam
published in: Siberian Mathematical Journal
publication date: 1997-11-10T00:00:00Z
review text: In former papers the averaging method was used for studying the problem of the onset of a convection flow in a fluid subject to high-frequency vertical vibrations, oblique vibrations, or vibrations in weightlessness. Mathematical justification of applicability of the method to such problems was carried out for vertical oscillations of a particular form and later for a broad class of vertical oscillations and oscillations in weightlessness. In the present article, we extend the justification to a broad class of vibrations acting in arbitrary directions. The results are exposed for some system of evolution differential equations which involves the above-indicated convection problems (as particular cases). We especially point out that here we essentially improve the earlier results in the framework of a more general problem. For instance, we considerably widen the scale that characterizes smoothness of the initial data of the problem, find out conditions under which (weak) solutions are classical, and study instability of solutions in more detail.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76M25
zbMATH DE Number: 1023910
zbMATH Keywords: weak solution
zbMATH Keywords: classical solution
zbMATH Keywords: averaging method
zbMATH Keywords: convection flow in a fluid
zbMATH Keywords: high-frequency vertical vibrations
zbMATH Keywords: oblique vibrations
zbMATH Keywords: vibrations in weightlessness
zbMATH Keywords: instability of solutions
MaRDI profile type: Publication
cites work: A JUSTIFICATION OF THE AVERAGING METHOD FOR A PROBLEM OF CONVECTION IN A FIELD OF RAPIDLY OSCILLATING FORCES AND FOR OTHER PARABOLIC EQUATIONS
cites work: Justification of the averaging method for the convection problem with high-frequency vibrations
cites work: Q3815682
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description: scientific article; zbMATH DE number 1023910