The Linear Sampling Method for Reconstructing a Penetrable Cavity with Unknown External Obstacles

被引：0
作者：
Jianguo Ye
Guozheng Yan
机构：
[1] Kashi University,Research Center of Modern Mathematics and Its Application, School of Mathematics and Statistics
[2] Central China Normal University,School of Mathematics and Statistics
来源：
Acta Mathematica Scientia | 2023年 / 43卷
关键词：
inverse scattering; mixed boundary value problem; exterior transmission eigenvalue; interior measurements; linear sampling method; 35P25; 35R30; 47A40;
D O I：
暂无
中图分类号：
学科分类号：
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.
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页码：751 / 776
页数：25
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[1]  
Hu Y Q(2014)The inverse scattering problem for a partially coated cavity with interior measurements Appl Anal 93 936-956
[2]  
Cakoni F(2011)An inverse electromagnetic scattering problem for a cavity Inverse Probl 27 125002-914
[3]  
Liu J J(2008)Testing the integrity of some cavity-the Cauchy problem and the range test Appl Numer Math 58 899-708
[4]  
Zeng F(2011)Nonlinear integral equations for shape reconstruction in the inverse interior scattering problem Inverse Probl 27 035005-174
[5]  
Cakoni F(2012)The inverse scattering problem for cavities Appl Numer Math 62 699-454
[6]  
Sun J G(2012)The inverse scattering problem for cavities with impedance boundary condition Adv Comput Math 36 157-30
[7]  
Jakubik P(2012)Reconstruction for cavities with impedance boundary condition J Integral Equa Appl 25 431-303
[8]  
Potthast R(2015)The interior inverse scattering problem for cavities with an artificial obstacle Appl Numer Math 88 18-1750
[9]  
Qin H H(2014)The factorization method for cavities Inverse Probl 30 015006-868
[10]  
Cakoni F(2013)A decomposition method for an interior inverse scattering problem Inverse Probl Imaging 7 291-299
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