UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

doi:10.1007/s10473-021-0318-7

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 925-940.doi: 10.1007/s10473-021-0318-7

UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

向建立, 严国政

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

收稿日期:2020-03-05 修回日期:2020-05-25 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Guozheng YAN E-mail:yangz@mail.ccnu.edu.cn
作者简介:Jianli XIANG,E-mail:xiangjl@mails.ccnu.edu.cn
基金资助:
This research is supported by NSFC (11571132).

UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

Jianli XIANG, Guozheng YAN

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2020-03-05 Revised:2020-05-25 Online:2021-06-25 Published:2021-06-07
Contact: Guozheng YAN E-mail:yangz@mail.ccnu.edu.cn
About author:Jianli XIANG,E-mail:xiangjl@mails.ccnu.edu.cn
Supported by:
This research is supported by NSFC (11571132).

摘要/Abstract

摘要： This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition. We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number. In the first part of this paper, adequate preparations for the main uniqueness result are made. We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves. Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method. Finally, the a priori estimates of solutions to the general transmission problem with boundary data in $L^{p}(\partial\Omega)$ ($1

关键词: Acoustic wave, uniqueness, mixed reciprocity relation, modified interior transmission problem, a priori estimates

Abstract: This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition. We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number. In the first part of this paper, adequate preparations for the main uniqueness result are made. We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves. Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method. Finally, the a priori estimates of solutions to the general transmission problem with boundary data in $L^{p}(\partial\Omega)$ ($1

Key words: Acoustic wave, uniqueness, mixed reciprocity relation, modified interior transmission problem, a priori estimates

中图分类号:

35P25

向建立, 严国政. UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION[J]. 数学物理学报(英文版), 2021, 41(3): 925-940.

Jianli XIANG, Guozheng YAN. UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION[J]. Acta mathematica scientia,Series B, 2021, 41(3): 925-940.

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UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

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