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

Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications

Huaian Diao
, Yueran Geng^*
, Hongyu Liu
, Qinghua Yu

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

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. © 2023, Global Science Press. All rights reserved.

Original language	English
Pages (from-to)	523-538
Journal	Communications in Mathematical Research
Volume	39
Issue number	4
Online published	7 Nov 2023
DOIs	https://doi.org/10.4208/cmr.2023-0014
Publication status	Published - Nov 2023

Funding

The work of H. Diao is supported by the National Natural Science Foundation of China (Grant No. 12371422) and the Fundamental Research Funds for the Central Universities, JLU (Grant No. 93Z172023Z01). The work of Y. Geng is supported by the Graduate Innovation Fund of Jilin University (Grant No. 2023CX276). The work of Hongyu Liu is supported by the Hong Kong RGC General Research Funds (Projects 12302919, 12301420 and 11300821), the NSFC/RGC Joint Research Fund (Project N City U101/21), the France-Hong Kong ANR/RGC Joint Research (Grant No. A-HKBU 203/19).

Research Keywords

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

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RGC-funded

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@article{8269a05d70294eed80e5098f18a0c364,

title = "Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications",

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 H{\"o}lder 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. {\textcopyright} 2023, Global Science Press. All rights reserved.",

keywords = "corner singularity, inverse scattering, Non-radiating sources, single far-field measurement, vanishing",

author = "Huaian Diao and Yueran Geng and Hongyu Liu and Qinghua Yu",

year = "2023",

month = nov,

doi = "10.4208/cmr.2023-0014",

language = "English",

volume = "39",

pages = "523--538",

number = "4",

}

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

PY - 2023/11

Y1 - 2023/11

N2 - 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. © 2023, Global Science Press. All rights reserved.

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. © 2023, Global Science Press. All rights reserved.

KW - corner singularity

KW - inverse scattering

KW - Non-radiating sources

KW - single far-field measurement

KW - vanishing

UR - https://www.scopus.com/pages/publications/105023697981

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-105023697981&origin=recordpage

U2 - 10.4208/cmr.2023-0014

DO - 10.4208/cmr.2023-0014

M3 - RGC 21 - Publication in refereed journal

SN - 1674-5647

VL - 39

SP - 523

EP - 538

JO - Communications in Mathematical Research

JF - Communications in Mathematical Research

IS - 4

ER -

Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications

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GRF: Mathematical Studies of Surface-localized Transmission Eigenstates and Applications

GRF: Geometric Properties of Three Classes of Spectral Problems with Applications to Inverse Problems and Material Sciences

GRF: Mathematical and Computational Studies of Geomagnetic Anomaly Detections

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