Recovery of small electromagnetic inhomogeneities from partial boundary measurements

Habib Ammari; Alexander G. Ramm

doi:10.1016/S1631-0721(02)01449-3

Recovery of small electromagnetic inhomogeneities from partial boundary measurements

Habib Ammari ¹; Alexander G. Ramm ²

¹ Centre de mathématiques appliquées, CNRS UMR 7641 & École polytechnique, 91128 Palaiseau cedex, France
² Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, USA

Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 199-205.

corrected-by Erratum entitled: Recovery of small electromagnetic inhomogeneities from partial boundary measurements published in Série IIb, t. 330, n^∘ 3, pp. 199–205

Abstract
Résumé

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data.

Nous considérons deux problèmes d'identification de petites inhomogénéités diélectriques à partir de mesures incomplètes. Pour chaque problème, nous construisons une fonction dont la transformée de Fourier inverse permet de localiser les petites inhomogénéités.

Received: 2002-02-05
Accepted: 2002-02-11
Published online: 2002-01-01

DOI: 10.1016/S1631-0721(02)01449-3

Keywords: continuum mechanics, Helmholtz equation, reconstruction problem, small dielectric inhomogeneities, partial measurements
Mots-clés : milieux continus, équation de Holmholtz, problème de reconstruction, petites inhomogénéités diélectriques, mesures partielles

Author's affiliations:

Habib Ammari ¹; Alexander G. Ramm ²

¹ Centre de mathématiques appliquées, CNRS UMR 7641 & École polytechnique, 91128 Palaiseau cedex, France
² Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, USA

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Habib Ammari; Alexander G. Ramm. Recovery of small electromagnetic inhomogeneities from partial boundary measurements. Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 199-205. doi : 10.1016/S1631-0721(02)01449-3. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01449-3/

References
Cited by

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