TY - JOUR T1 - Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications AU - Diao , Huaian AU - Geng , Yueran AU - Liu , Hongyu AU - Yu , Qinghua JO - Communications in Mathematical Research VL - 4 SP - 523 EP - 538 PY - 2023 DA - 2023/11 SN - 39 DO - http://doi.org/10.4208/cmr.2023-0014 UR - https://global-sci.org/intro/article_detail/cmr/22099.html KW - Non-radiating sources, corner singularity, vanishing, inverse scattering, single far-field measurement. AB -

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.