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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Three-phase eccentric annulus subjected to a potential field induced by arbitrary singularities


Author: Yu. V. Obnosov
Journal: Quart. Appl. Math. 69 (2011), 771-786
MSC (2010): Primary 30E25, 76T30
Published electronically: July 12, 2011
MathSciNet review: 2894000
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Abstract: An infinite planar, three-component heterogeneous medium with a pair of circles as interfaces between homogeneous zones forming an eccentric annulus is considered for refraction of a potential field on the two interfaces. The velocity field is generated by an arbitrary system of singularities of arbitrary order, in congruity with the Milne-Thomson case of a two-component medium and a single circular interface. An exact analytical solution of the corresponding $ {\mathbb{R}}$-linear conjugation problem of two Laplacian fields in the eccentrical annulus structure is derived in the class of piecewise meromorphic functions with fixed principal part. Three general cases of loci of the singularities with respect to the interfaces are investigated. Flow nets (isobars and streamlines) are presented.


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Additional Information

Yu. V. Obnosov
Affiliation: Institute of Mathematics and Mechanics, Kazan State University, Prof. Nughin Str.,1/37, Kazan, 420008, Russia
Email: Yurii.Obnosov@ksu.ru

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01242-8
PII: S 0033-569X(2011)01242-8
Keywords: Refraction, heterogeneous media, $\mathbb R$-linear conjugation problem, analytic functions
Received by editor(s): May 3, 2010
Published electronically: July 12, 2011
Article copyright: © Copyright 2011 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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