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Local and global existence results for anisotropic Hele–Shaw flows

Published online by Cambridge University Press:  14 November 2011

Klaus Deckelnick  and
Charles M. Elliott
Klaus Deckelnick
Affiliation:
Centre for Mathematical Analysis and its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
Charles M. Elliott
Affiliation:
Centre for Mathematical Analysis and its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK
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Abstract

In this paper we study a moving boundary problem for an anisotropic two-phase Hele–Shaw flow. Using a regularization technique, we prove existence of a local solution. Under suitable conditions on the initial free boundary we obtain a global solution and study its asymptotic behaviour.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 2 , 1999 , pp. 265 - 294
Copyright
Copyright © Royal Society of Edinburgh 1999

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