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The Interior Transmission Eigenvalue Problem for Absorbing Media

Fioralba Cakoni 1 David Colton 1 Houssem Haddar 2 
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : In recent years, the transmission eigenvalue problem has been extensively studied for non-absorbing media. In this paper, we initiate the study of this problem for absorbing media. In particular, we show that, in the case of absorbing media, transmission eigenvalues form a discrete set, exist for sufficiently small absorption and for spherically stratified media exist without this assumption. For constant index of refraction, we also obtain regions in the complex plane where the transmission eigenvalues cannot exist and obtain a priori estimates for real transmission eigenvalues.
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Submitted on : Sunday, October 14, 2012 - 11:15:28 PM
Last modification on : Friday, November 18, 2022 - 9:26:50 AM

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Fioralba Cakoni, David Colton, Houssem Haddar. The Interior Transmission Eigenvalue Problem for Absorbing Media. Inverse Problems, 2012, 28 (4), pp.045005. ⟨10.1088/0266-5611/28/4/045005⟩. ⟨hal-00741619⟩



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