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

被引：2
|
作者：
Ye, Jianguo [1 ]
Yan, Guozheng [2 ]
机构：
[1] Kashi Univ, Res Ctr Modern Math & Its Applicat, Sch Math & Stat, Kashi 844000, Peoples R China
[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2023年 / 43卷 / 02期
关键词：
inverse scattering; mixed boundary value problem; exterior transmission eigenvalue; interior measurements; linear sampling method; INVERSE SCATTERING PROBLEM;
D O I：
10.1007/s10473-023-0216-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
引用
收藏
页码：751 / 776
页数：26
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