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Moving boundary problems and non-uniqueness for the thin film equation

Published online by Cambridge University Press:  06 August 2001

J. R. KING  and
M. BOWEN
J. R. KING
Affiliation:
Division of Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
M. BOWEN
Affiliation:
Mathematical Institute, Leiden University, PO Box 9512, The Netherlands
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Abstract

A variety of mass preserving moving boundary problems for the thin film equation, ut = −(unuxxx)x, are derived (by formal asymptotics) from a number of regularisations, the case in which the substrate is covered by a very thin pre-wetting film being discussed in most detail. Some of the properties of the solutions selected in this fashion are described, and the full range of possible mass preserving non-negative solutions is outlined.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 12 , Issue 3 , June 2001 , pp. 321 - 356
Copyright
© 2001 Cambridge University Press

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