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Stability of self-similar extinction solutions for a 3D Darcy flow suction problem

Published online by Cambridge University Press:  01 August 2009

ERWIN VONDENHOFF  and
GEORG PROKERT
ERWIN VONDENHOFF
Affiliation:
Eindhoven University of Technology, Department of Mathematics and Computer Science P.O. Box 513, 5600 MB Eindhoven, The Netherlands emails: e.vondenhoff@tue.nl, g.prokert@tue.nl
GEORG PROKERT
Affiliation:
Eindhoven University of Technology, Department of Mathematics and Computer Science P.O. Box 513, 5600 MB Eindhoven, The Netherlands emails: e.vondenhoff@tue.nl, g.prokert@tue.nl
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Abstract

We present a stability result for a class of non-trivial self-similarly vanishing solutions to a 3D Hele-Shaw moving boundary problem with surface tension and single-point suction. These solutions are domains that bifurcate from the trivial spherical solution. The moving domains have a geometric centre located at the suction point and they are axially symmetric. We show stability with respect to perturbations that preserve these properties.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 20 , Issue 4 , August 2009 , pp. 343 - 362
Copyright
Copyright © Cambridge University Press 2009

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