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Asymptotic expansions for the voltage potentials with two‐dimensional and three‐dimensional thin interfaces
Author(s) -
Khelifi Abdessatar,
Zribi Habib
Publication year - 2011
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.1529
Subject(s) - mathematics , conductivity , voltage , thin layer , mathematical analysis , asymptotic expansion , steady state (chemistry) , layer (electronics) , asymptotic analysis , physics , materials science , chemistry , nanotechnology , quantum mechanics
We derive asymptotic formulae for two‐dimensional and three‐dimensional steady state voltage potentials associated with thin conductivity imperfections having no uniform thickness. These formulae recover highly conducting inclusions and those with interfacial resistance. Our calculations are rigorous and based on layer potential techniques. Copyright © 2011 John Wiley & Sons, Ltd.