Nonradiating sources and transmission eigenfunctions vanish at corners\n and edges

2018/03/28 by Blåsten, Eemeli · 4 citations
Computer Science · Engineering · Mathematics · #35P25 #51M20 #78A46 (primary) #81V80 (secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1803.10917

openalex publication_date 2018/03/28 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider the inverse source problem of a fixed wavenumber: study\nproperties of an acoustic source based on a single far- or near-field\nmeasurement. We show that nonradiating sources having a convex or non-convex\ncorner or edge on their boundary must vanish there. The same holds true for\nsmooth enough transmission eigenfunctions. The proof is based on an energy\nidentity from the enclosure method and the construction of a new type of planar\ncomplex geometrical optics solution whose logarithm is a branch of the square\nroot. The latter allows us to deal with non-convex corners and edges.\n

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