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A variational inequality approach to Hele-Shaw flow with a moving boundary

Published online by Cambridge University Press:  14 November 2011

C. M. Elliott  and
V. Janovský
C. M. Elliott
Affiliation:
Imperial College, London
V. Janovský
Affiliation:
Charles University, Prague
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Synopsis

This paper is concerned with the study of a mathematical model of the injection of fluid into a finite Hele–Shaw cell. The mathematical problem is one of solving Laplace's equation in an unknown region whose boundary changes with time. By a transformation of the dependent variable, an elliptic variational inequality formulation of the moving boundary problem is obtained. The variational inequality is shown to have a unique solution up to the time at which the cell is filled. Regularity results for the solution of the inequality are obtained by studying a penalty approximation of the inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 1-2 , 1981 , pp. 93 - 107
Copyright
Copyright © Royal Society of Edinburgh 1981

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