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

作　　者：Huaian Diao Yueran Geng Hongyu Liu Qinghua Yu 

机构地区：[1]School of Mathematics and Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University,Changchun,Jilin 130012,P.R.China. [2]Department of Mathematics,City University of Hong Kong,Kowloon,Hong Kong SAR,P.R.China. [3]The School Attached to Dalian Maritime University,Dalian 116000,P.R.China.

出　　处：《Communications in Mathematical Research》2023年第4期523-538,共16页数学研究通讯（英文版）

基　　金：the National Natural Science Foundation of China(Grant No.12371422);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 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/RGCJoint Research(Grant No.A-HKBU 203/19).

摘　　要：Considering the acoustic source scattering problems,when the sour-ce 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 Holder 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.

关 键 词：Non-radiating sources corner singularity VANISHING inverse scattering sin-gle far-field measurement 

分 类 号：O189[理学—数学] O177[理学—基础数学]