Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications
Year: 2023
Author: Huaian Diao, Yueran Geng, Hongyu Liu, Qinghua Yu
Communications in Mathematical Research , Vol. 39 (2023), Iss. 4 : pp. 523–538
Abstract
Considering the acoustic source scattering problems, when the source is non-radiating/invisible, we investigate the geometrical characterization for the underlying sources at polyhedral and conical corner. It is revealed that the non-radiating source with Hölder continuous regularity must vanish at the corner. Using this kind of geometrical characterization of non-radiating sources, we establish local and global unique determination for a source with the polyhedral or corona shape support by a single far field measurement. Uniqueness by a single far field measurement constitutes of a long standing problem in inverse scattering problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2023-0014
Communications in Mathematical Research , Vol. 39 (2023), Iss. 4 : pp. 523–538
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Non-radiating sources corner singularity vanishing inverse scattering single far-field measurement.