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Asymptotic behaviour of the thin film equation in bounded domains

Published online by Cambridge University Press:  15 June 2001

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

We investigate the extinction behaviour of a fourth order degenerate diffusion equation in a bounded domain, the model representing the flow of a viscous fluid over edges at which zero contact angle conditions hold. The extinction time may be finite or infinite and we distinguish between the two cases by identification of appropriate similarity solutions. In certain cases, an unphysical mass increase may occur for early time and the solution may become negative; an appropriate remedy for this is noted. Numerical simulations supporting the analysis are included.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 12 , Issue 2 , April 2001 , pp. 135 - 157
Copyright
2001 Cambridge University Press

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