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Asymptotics of Hele-Shaw flows with multiple point sources

Published online by Cambridge University Press:  08 December 2010

Michiaki Onodera
Michiaki Onodera
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
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Abstract

We study the asymptotic behaviour of a Hele-Shaw flow produced by the injection of fluid from a finite number of points at different speeds. We prove that, as time tends to infinity, the boundary of the fluid domain approaches the circle centred at the barycentre of the injection points with weights proportional to the injection rates. The distances from the barycentre to the boundary points are estimated from both above and below.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 6 , December 2010 , pp. 1217 - 1247
Copyright
Copyright © Royal Society of Edinburgh 2010

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