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MOVING STONE IN THE HELE-SHAW FLOW

Part of:Elliptic equations and systemsIncompressible viscous fluidsMiscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  08 April 2015

Gennady Mishuris,
Sergei Rogosin and
Michal Wrobel
Gennady Mishuris
Affiliation:
Aberystwyth University, Penglais, Aberystwyth SY23 3BZ, U.K. email ggm@aber.ac.uk
Sergei Rogosin
Affiliation:
Aberystwyth University, Penglais, Aberystwyth SY23 3BZ, U.K. email ser14@aber.ac.ukBelarusian State University, Nezavisimosti Ave., 4, 220030 Minsk, Belarus email rogosin@bsu.by
Michal Wrobel
Affiliation:
Aberystwyth University, Penglais, Aberystwyth SY23 3BZ, U.K. email miw15@aber.ac.uk

Abstract

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Asymptotic analysis of the Hele-Shaw flow with a small moving obstacle is performed. The method of solution utilizes the uniform asymptotic formulas for Green’s and Neumann functions recently obtained by V. Maz’ya and A. Movchan. The theoretical results of the paper are illustrated by numerical simulations.

MSC classification

Primary:76D27: Other free-boundary flows; Hele-Shaw flows35J25: Boundary value problems for second-order elliptic equations35R35: Free boundary problems

Information

Type
Research Article
Information
Mathematika , Volume 61 , Issue 2 , May 2015, pp. 457 - 474
Copyright
Copyright © University College London 2015 

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