Comptes Rendus
Recovery of small electromagnetic inhomogeneities from partial boundary measurements
[Identification de petites inhomogénéités diélectriques à partir de mesures partielles]
Comptes Rendus. Mécanique, Volume 330 (2002) no. 3, pp. 199-205.

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 :
Accepté le :
Publié le :
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

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
@article{CRMECA_2002__330_3_199_0,
     author = {Habib Ammari and Alexander G. Ramm},
     title = {Recovery of small electromagnetic inhomogeneities from partial boundary measurements},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {199--205},
     publisher = {Elsevier},
     volume = {330},
     number = {3},
     year = {2002},
     doi = {10.1016/S1631-0721(02)01449-3},
     language = {en},
}
TY  - JOUR
AU  - Habib Ammari
AU  - Alexander G. Ramm
TI  - Recovery of small electromagnetic inhomogeneities from partial boundary measurements
JO  - Comptes Rendus. Mécanique
PY  - 2002
SP  - 199
EP  - 205
VL  - 330
IS  - 3
PB  - Elsevier
DO  - 10.1016/S1631-0721(02)01449-3
LA  - en
ID  - CRMECA_2002__330_3_199_0
ER  - 
%0 Journal Article
%A Habib Ammari
%A Alexander G. Ramm
%T Recovery of small electromagnetic inhomogeneities from partial boundary measurements
%J Comptes Rendus. Mécanique
%D 2002
%P 199-205
%V 330
%N 3
%I Elsevier
%R 10.1016/S1631-0721(02)01449-3
%G en
%F CRMECA_2002__330_3_199_0
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/

[1] M. Vogelius; D. Volkov Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities, Math. Model. Numer. Anal., Volume 34 (2000), pp. 723-748

[2] A.P. Calderón On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, Soc. Brasileira de Matemática, Rio de Janeiro, 1980, pp. 65-73

[3] J. Sylvester; G. Uhlmann A global uniqueness theorem for an inverse boundary value problem, Ann. Math., Volume 125 (1987), pp. 153-169

[4] D. Isaacson; E.L. Isaacson Comments on Calderón's paper: “On an inverse boundary value problem”, Math. Compt., Volume 52 (1989), pp. 553-559

[5] H. Ammari, S. Moskow, M. Vogelius, Boundary integral formulas for the reconstruction of electromagnetic imperfections of small diameter, ESAIM: Cont. Opt. Calc. Var., to appear

[6] H. Ammari, An inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume, SIAM J. Control Optim., to appear

[7] R. Kohn; M. Vogelius Determining conductivity by boundary measurements, Comm. Pure Appl. Math., Volume 37 (1984), pp. 289-298

[8] A.L. Bukhgeim, G. Uhlmann, Recovering a potential from partial Cauchy data, Preprint

Cité par Sources :

Commentaires - Politique