Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area

Elena Beretta; Arup Mukherjee; Michael Vogelius

doi:10.1007/PL00001561

Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area

Elena Beretta, Arup Mukherjee, Michael Vogelius

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive asymptotic formulas for two dimensional steady state voltage potentials associated with thin, "curve-like" conductivity imperfections. Our derivation is formal, and based on asymptotic matching of terms in an appropriate set of integral equations. In combination with the formulas (rigorously) derived in [3] for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

Original language	English (US)
Pages (from-to)	543-572
Number of pages	30
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	52
Issue number	4
DOIs	https://doi.org/10.1007/PL00001561
State	Published - Jul 2001

Keywords

Asymptotic formulas
Inverse conductivity problem
Thin imperfections

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy
Applied Mathematics

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10.1007/PL00001561

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abstract = "We derive asymptotic formulas for two dimensional steady state voltage potentials associated with thin, {"}curve-like{"} conductivity imperfections. Our derivation is formal, and based on asymptotic matching of terms in an appropriate set of integral equations. In combination with the formulas (rigorously) derived in [3] for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.",

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author = "Elena Beretta and Arup Mukherjee and Michael Vogelius",

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AU - Mukherjee, Arup

AU - Vogelius, Michael

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Y1 - 2001/7

N2 - We derive asymptotic formulas for two dimensional steady state voltage potentials associated with thin, "curve-like" conductivity imperfections. Our derivation is formal, and based on asymptotic matching of terms in an appropriate set of integral equations. In combination with the formulas (rigorously) derived in [3] for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

AB - We derive asymptotic formulas for two dimensional steady state voltage potentials associated with thin, "curve-like" conductivity imperfections. Our derivation is formal, and based on asymptotic matching of terms in an appropriate set of integral equations. In combination with the formulas (rigorously) derived in [3] for imperfections of small diameter, these new formulas cover the generic imperfections of small area in two dimensions.

KW - Asymptotic formulas

KW - Inverse conductivity problem

KW - Thin imperfections

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Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area

Abstract

Keywords

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