Journal article
A NOTE ON TRANSMISSION EIGENVALUES IN
Inverse problems and imaging (Springfield, Mo.), v 15(5), pp 999-1014
01 Oct 2021
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
This short note was motivated by our efforts to investigate whether there exists a half plane free of transmission eigenvalues for Maxwell's equations. This question is related to solvability of the time domain interior transmission problem which plays a fundamental role in the justification of linear sampling and factorization methods with time dependent data. Our original goal was to adapt semiclassical analysis techniques developed in [21, 23] to prove that for some combination of electromagnetic parameters, the transmission eigenvalues lie in a strip around the real axis. Unfortunately we failed. To try to understand why, we looked at the particular example of spherically symmetric media, which provided us with some insight on why we couldn't prove the above result. Hence this paper reports our findings on the location of all transmission eigenvalues and the existence of complex transmission eigenvalues for Maxwell's equations for spherically stratified media. We hope that these results can provide reasonable conjectures for general electromagnetic media.
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Details
- Title
- A NOTE ON TRANSMISSION EIGENVALUES IN
- Creators
- Fioralba Cakoni - Rutgers, The State University of New JerseyShixu Meng - Academy of Mathematics and Systems ScienceJingni Xiao - Rutgers, The State University of New Jersey
- Publication Details
- Inverse problems and imaging (Springfield, Mo.), v 15(5), pp 999-1014
- Publisher
- Amer Inst Mathematical Sciences-Aims
- Number of pages
- 16
- Grant note
- DMS-1813492 / NSF; National Science Foundation (NSF) FA9550-20-1-0024 / AFOSR; United States Department of Defense; Air Force Office of Scientific Research (AFOSR)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000683552600008
- Scopus ID
- 2-s2.0-85114292028
- Other Identifier
- 991021878115204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical