UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN*

doi:10.1007/s10473-023-0125-4

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 450-468.doi: 10.1007/s10473-023-0125-4

• • 上一篇

UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN^*

Jianli XIANG¹, Guozheng YAN^2,†

1. Three Gorges Mathematical Research Center, College of Science, China Three Gorges University, Yichang 443002, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

收稿日期:2021-04-05 修回日期:2022-06-11 发布日期:2023-03-01
通讯作者: †Guozheng YAN. E-mail: yangz@ccnu.edu.cn
基金资助:
*NSFC (11571132).

UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN^*

Jianli XIANG¹, Guozheng YAN^2,†

1. Three Gorges Mathematical Research Center, College of Science, China Three Gorges University, Yichang 443002, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2021-04-05 Revised:2022-06-11 Published:2023-03-01
Contact: †Guozheng YAN. E-mail: yangz@ccnu.edu.cn
About author:Jianli XIANG,E-mail: xiangjianli@ctgu.edu.cn
Supported by:
*NSFC (11571132).

摘要/Abstract

摘要： In this paper, we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency. It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so it is impossible to reconstruct the location of the underlying scatterers. Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium, we consider different types of superpositions of incident waves to break the translation invariance property.

关键词: conductive boundary condition, uniqueness, phaseless far field data, inverse scattering

Abstract: In this paper, we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency. It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so it is impossible to reconstruct the location of the underlying scatterers. Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium, we consider different types of superpositions of incident waves to break the translation invariance property.

Key words: conductive boundary condition, uniqueness, phaseless far field data, inverse scattering

Jianli XIANG, Guozheng YAN. UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN^*[J]. 数学物理学报(英文版), 2023, 43(1): 450-468.

Jianli XIANG, Guozheng YAN. UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 450-468.

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UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN^*

UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN^*

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