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Journal article
ON AN ELECTROMAGNETIC PROBLEM IN A CORNER AND ITS APPLICATIONS
Analysis & PDE, v 14(7), pp 2207-2224
01 Jan 2021
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
Let K-x0(r0) be a (nondegenerate) truncated corner in R-3, with x(0) is an element of R-3 being its apex, and F-j is an element of C-alpha(<(K-x0(r0))over bar>, C-3), j = 1, 2, where alpha is the positive Holder index. Consider the electromagnetic problem
{del boolean AND E - i omega mu H-0 = F-1 in K-x0(r0),
del boolean AND H - i omega epsilon E-0 = F-2 in K-x0(r0),
nu boolean AND E = nu boolean AND H = 0 on partial derivative K-x0(r0) \ partial derivative B-r0(x(0)),
where nu denotes the exterior unit normal vector of partial derivative K-x0(r0). We prove that F-1 and F-2 must vanish at the apex x(0). There is a series of interesting consequences of this vanishing property in several separate but intriguingly connected topics in electromagnetism. First, we can geometrically characterize nonradiating sources in time-harmonic electromagnetic scattering. Secondly, we consider the inverse source scattering problem for time-harmonic electromagnetic waves and establish the uniqueness result in determining the polyhedral support of a source by a single far-field measurement. Thirdly, we derive a property of the geometric structure of electromagnetic interior transmission eigenfunctions near corners. Finally, we also discuss its implication to invisibility cloaking and inverse medium scattering.
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Details
- Title
- ON AN ELECTROMAGNETIC PROBLEM IN A CORNER AND ITS APPLICATIONS
- Creators
- Emilia Blasten - Aalto UniversityHongyu Liu - City University of Hong KongJingni Xiao - Rutgers, The State University of New Jersey
- Publication Details
- Analysis & PDE, v 14(7), pp 2207-2224
- Publisher
- Mathematical Science Publ
- Number of pages
- 18
- Grant note
- 12302017; 12301218; 12302919 / Hong Kong RGC General Research Funds City University of Hong Kong PRG 832 / Estonian Research Council 312124 / Academy of Finland; Research Council of Finland
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000733976600008
- Scopus ID
- 2-s2.0-85123514381
- Other Identifier
- 991021878014904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied