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The Kelvin transformation as a tool for analyzing problems in medicine and technology
Author(s) -
Baganis G.,
Dassios G.,
Hadjinicolaou M.,
Protopapas E.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2903
Subject(s) - mathematics , transformation (genetics) , conservative vector field , flow (mathematics) , mathematical analysis , classical mechanics , physics , geometry , mechanics , compressibility , biochemistry , chemistry , gene
The well‐known Kelvin transformation for harmonic functions has been employed in order to derive solutions for the Dirichlet and Neumann problems for the case of nonconvex domains such as the inverted triangle. In addition, Kelvin's transformation has been extended to the irrotational and rotational Stokes flows. This enables us to derive solutions for problems arising in Medicine and Physiology, including blood flow and the sedimentation of red blood cells, potential problems in acoustic scattering and electrostatics, as well as other problems that cannot be solved by the standard spectral methods. Copyright © 2013 John Wiley & Sons, Ltd.