Qualitative Analysis of Coating Flows on a Rotating Horizontal Cylinder

We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of gravity. The parameters involved determine a rich variety of qual...

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Bibliographic Details
Published in:International journal of differential equations 2012-01, Vol.2012 (2012), p.1-30
Main Authors: Chugunova, Marina, Taranets, Roman M.
Format: Article
Language:English
Subjects:
Cylinders
Differential equations
Gravity
Horizontal
Inequality
Liquid films
Mathematical analysis
Mathematical models
Protective coatings
Reynolds number
Rotating
Studies
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Summary:We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of gravity. The parameters involved determine a rich variety of qualitatively different flows. We obtain sufficient conditions for finite speed of support propagation and for waiting time phenomena by application of a new extension of Stampacchia's lemma for a system of functional equations.
ISSN:1687-9643
1687-9651
DOI:10.1155/2012/570283