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Journal article
THE PERTURBATION OF TRANSMISSION EIGENVALUES FOR INHOMOGENEOUS MEDIA IN THE PRESENCE OF SMALL PENETRABLE INCLUSIONS
Inverse problems and imaging (Springfield, Mo.), v 9(3), pp 725-748
01 Aug 2015
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Abstract
This paper concerns the transmission eigenvalue problem for an inhomogeneous media of compact support containing small penetrable homogeneous inclusions. Assuming that the inhomogeneous background media is known and smooth, we investigate how these small volume inclusions affect the real transmission eigenvalues. Note that for practical applications the real transmission eigenvalues are important since they can be measured from the scattering data. In particular, in addition to proving the convergence rate for the eigenvalues corresponding to the perturbed media as inclusions' volume goes to zero, we also provide the explicit first correction term in the asymptotic expansion for simple eigenvalues. The correction terms involves the eigenvalues and eigenvectors of the unperturbed known background as well as information about the location, size and refractive index of small inhomogeneities. Thus, our asymptotic formula has the potential to be used to recover information about small inclusions from a knowledge of real transmission eigenvalues.
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Details
- Title
- THE PERTURBATION OF TRANSMISSION EIGENVALUES FOR INHOMOGENEOUS MEDIA IN THE PRESENCE OF SMALL PENETRABLE INCLUSIONS
- Creators
- Fioralba Cakoni - Florida State UniversityShari Moskow - Drexel UniversityScott Rome - Drexel Univ, Dept Math, Philadelphia, PA 19104 USA
- Publication Details
- Inverse problems and imaging (Springfield, Mo.), v 9(3), pp 725-748
- Publisher
- Amer Inst Mathematical Sciences-Aims
- Number of pages
- 24
- Grant note
- FA9550-13-1-0199 / Air Force Office of Scientific Research Grant; United States Department of Defense; Air Force Office of Scientific Research (AFOSR) DMS-1108858; DMS -1411721 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000360672300005
- Scopus ID
- 2-s2.0-84938493744
- Other Identifier
- 991019167857604721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical