Conductivity interface problems. Part I: Small perturbations of an interface
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- by Habib Ammari, Hyeonbae Kang, Mikyoung Lim and Habib Zribi PDF
- Trans. Amer. Math. Soc. 362 (2010), 2435-2449 Request permission
Abstract:
We derive high-order terms in the asymptotic expansions of boundary perturbations of steady-state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion with ${\mathcal C}^2$-boundary. Our derivation is rigorous and based on layer potential techniques. The asymptotic expansion in this paper is valid for ${\mathcal C}^1$-perturbations and inclusions with extreme conductivities. It extends those already derived for small volume conductivity inclusions and leads us to very effective algorithms for determining lower-order Fourier coefficients of the shape perturbation of the inclusion based on boundary measurements. We perform some numerical experiments using the algorithm to test its effectiveness.References
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Additional Information
- Habib Ammari
- Affiliation: Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France
- MR Author ID: 353050
- Email: ammari@cmapx.polytechnique.fr
- Hyeonbae Kang
- Affiliation: Department of Mathematical Sciences and RIM, Seoul National University, Seoul 151-747, Korea
- Address at time of publication: Department of Mathematics, Inha University, Incheon 402-751, Korea
- MR Author ID: 268781
- Email: hkang@math.snu.ac.kr, hbkang@inha.ac.kr
- Mikyoung Lim
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- Address at time of publication: Department of Mathematical Sciences, Korean Advanced Institute of Science and Technology, 335 Gwahangno (373-1 Gueseong-dong), Yuseong-gu, Daejeon 305-701, Korea
- MR Author ID: 689036
- Email: lim@math.colostate.edu, mklim@kaist.ac.kr
- Habib Zribi
- Affiliation: Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France
- Address at time of publication: Department of Mathematical Sciences, Korean Advanced Institute of Science and Technology, 335 Gwahangno (373-1 Gueseong-dong), Yuseong-gu, Daejeon 305-701, Korea
- Email: zribi@cmapx.polytechnique.fr
- Received by editor(s): January 13, 2006
- Received by editor(s) in revised form: January 27, 2008
- Published electronically: December 16, 2009
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 362 (2010), 2435-2449
- MSC (2000): Primary 35B30
- DOI: https://doi.org/10.1090/S0002-9947-09-04842-9
- MathSciNet review: 2584606