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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
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

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
Copyright
Copyright © Cambridge University Press 2009

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