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Solutions of a free boundary problem in a doubly connected domain via a circular-arc polygon

Published online by Cambridge University Press:  06 June 2014

J. S. MARSHALL
J. S. MARSHALL*
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK email: jonathan.marshall1@imperial.ac.uk
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Abstract

This paper addresses a free boundary problem for a steady, uniform patch of vorticity surrounding a single flat plate of zero thickness and finite length. Exact solutions to this problem have previously been found in terms of conformal maps represented by Cauchy-type integrals. Here, however, it is demonstrated how, by considering an associated circular-arc polygon and using ideas from automorphic function theory, these maps can be expressed in a simple non-integral form.

Keywords

Free boundary problemMultiply connectedConformal mappingAutomorphic functions

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 5 , October 2014 , pp. 579 - 594
Copyright
Copyright © Cambridge University Press 2014 

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