International Journal of Differential Equations
Volume 2012 (2012), Article ID 570283, 30 pages
Research Article

Qualitative Analysis of Coating Flows on a Rotating Horizontal Cylinder

1School of Mathematical Sciences, Claremont Graduate University, 710 N. College Avenue, Claremont, CA 91711, USA
2School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

Received 11 May 2012; Accepted 1 August 2012

Academic Editor: Sining Zheng

Copyright © 2012 Marina Chugunova and Roman M. Taranets. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.