# The interior transmission eigenvalue problem for absorbing media

Fioralba Cakoni, David Colton, Houssem Haddar

Research output: Contribution to journalArticle

18 Citations (Scopus)

### 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.

Original language English (US) 045005 Inverse Problems 28 4 https://doi.org/10.1088/0266-5611/28/4/045005 Published - Apr 1 2012 Yes

### Fingerprint

Transmission Problem
Absorbing
Eigenvalue Problem
Interior
Eigenvalue
Refraction
A Priori Estimates
Argand diagram
Absorption

### All Science Journal Classification (ASJC) codes

• Theoretical Computer Science
• Signal Processing
• Applied Mathematics
• Computer Science Applications
• Mathematical Physics

### Cite this

Cakoni, Fioralba ; Colton, David ; Haddar, Houssem. / The interior transmission eigenvalue problem for absorbing media. In: Inverse Problems. 2012 ; Vol. 28, No. 4.
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The interior transmission eigenvalue problem for absorbing media. / Cakoni, Fioralba; Colton, David; Haddar, Houssem.

In: Inverse Problems, Vol. 28, No. 4, 045005, 01.04.2012.

Research output: Contribution to journalArticle

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