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The self-similar solution for draining in the thin film equation

Published online by Cambridge University Press:  01 September 2004

JAN BOUWE VAN DEN BERG ,
MARK BOWEN ,
JOHN R. KING  and
M. M. A. EL-SHEIKH
JAN BOUWE VAN DEN BERG
Affiliation:
Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands email: [email protected]
MARK BOWEN
Affiliation:
Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK email: [email protected], [email protected]
JOHN R. KING
Affiliation:
Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK email: [email protected], [email protected]
M. M. A. EL-SHEIKH
Affiliation:
Department of Mathematics, Faculty of Sciences, Menoufia University, Shibin El-Koom, Egypt
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Abstract

We investigate self-similar solutions of the thin film equation in the case of zero contact angle boundary conditions on a finite domain. We prove existence and uniqueness of such a solution and determine the asymptotic behaviour as the exponent in the equation approaches the critical value at which zero contact angle boundary conditions become untenable. Numerical and power-series solutions are also presented.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 15 , Issue 3 , June 2004 , pp. 329 - 346
Copyright
2004 Cambridge University Press

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