THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES*

doi:10.1007/s10473-023-0216-2

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (2): 751-776.doi: 10.1007/s10473-023-0216-2

THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES^*

Jianguo Ye¹, Guozheng Yan^2,†

1. Research Center of Modern Mathematics and Its Application, School of Mathematics and Statistics, Kashi University, Kashi 844000, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

收稿日期:2020-08-19 修回日期:2022-04-26 出版日期:2023-03-25 发布日期:2023-04-12
通讯作者: †Guozheng YAN, E-mail: yangz@ccnu.edu.cn.
作者简介:Jianguo YE, E-mail: yjgks2001@hotmail.com
基金资助:
The first author was supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (2019D01A05); The second author was supported by the NSFC (11571132).

THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES^*

Jianguo Ye¹, Guozheng Yan^2,†

1. Research Center of Modern Mathematics and Its Application, School of Mathematics and Statistics, Kashi University, Kashi 844000, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2020-08-19 Revised:2022-04-26 Online:2023-03-25 Published:2023-04-12
Contact: †Guozheng YAN, E-mail: yangz@ccnu.edu.cn.
About author:Jianguo YE, E-mail: yjgks2001@hotmail.com
Supported by:
The first author was supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (2019D01A05); The second author was supported by the NSFC (11571132).

摘要/Abstract

摘要： We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources. In the first part, we obtain the well-posedness of the direct scattering problem by the variational method. In the second part, we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity, and the shape of the external obstacle, however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.

关键词: inverse scattering, mixed boundary value problem, exterior transmission eigenvalue, interior measurements, linear sampling method

Abstract: We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources. In the first part, we obtain the well-posedness of the direct scattering problem by the variational method. In the second part, we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity, and the shape of the external obstacle, however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.

Key words: inverse scattering, mixed boundary value problem, exterior transmission eigenvalue, interior measurements, linear sampling method

Jianguo Ye, Guozheng Yan. THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES^*[J]. 数学物理学报(英文版), 2023, 43(2): 751-776.

Jianguo Ye, Guozheng Yan. THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES^*[J]. Acta mathematica scientia,Series B, 2023, 43(2): 751-776.

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THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES^*

THE LINEAR SAMPLING METHOD FOR RECONSTRUCTING A PENETRABLE CAVITY WITH UNKNOWN EXTERNAL OBSTACLES^*

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