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Volume 39, Issue 4
Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications

Huaian Diao, Yueran Geng, Hongyu Liu & Qinghua Yu

DOI: 10.4208/cmr.2023-0014

Commun. Math. Res., 39 (2023), pp. 523-538.

Published online: 2023-11

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  • 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.

  • Keywords

Non-radiating sources, corner singularity, vanishing, inverse scattering, single far-field measurement.

  • AMS Subject Headings

35Q60, 378A46, 35P2

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-523, author = {Diao , HuaianGeng , YueranLiu , Hongyu and Yu , Qinghua}, title = {Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {4}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0014}, url = {http://global-sci.org/intro/article_detail/cmr/22099.html} }
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.

Huaian Diao, Yueran Geng, Hongyu Liu & Qinghua Yu. (2023). Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications. Communications in Mathematical Research . 39 (4). 523-538. doi:10.4208/cmr.2023-0014
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