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Persistence of corners in free boundaries in Hele-Shaw flow

Published online by Cambridge University Press:  26 September 2008

J. R. King ,
A. A. Lacey  and
J. L. Vazquez
J. R. King
Affiliation:
Department of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD, UK
A. A. Lacey
Affiliation:
Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK
J. L. Vazquez
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
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Abstract

In this paper we investigate the movement of free boundaries in the two-dimensional Hele-Shaw problem. By means of the construction of special solutions of self-similar type we can describe the evolution of free boundary corners in terms of the angle at the corner. In particular, we prove that, in the injection case, while obtuse-angled corners move and smooth out instantaneously, acute-angled corners persist until a (finite) waiting time at which, at least for the special solutions, they suddenly jump into an obtuse angle, precisely the supplement of the original one. The critical values of the angle π and π/2 are also considered.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 5 , October 1995 , pp. 455 - 490
Copyright
Copyright © Cambridge University Press 1995

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