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
[Identification de petites inhomogénéités diélectriques à partir de mesures partielles]

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.

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

Résumé
Abstract

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.

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.

Reçu le : 2002-02-05
Accepté le : 2002-02-11
Publié le : 2002-01-01

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

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

Affiliations des auteurs :

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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     title = {Recovery of small electromagnetic inhomogeneities from partial boundary measurements},
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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/

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