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.
作者
叶建国
严国政
Jianguo YE;Guozheng YAN(Research Center of Modern Mathematics and Its Application,School of Mathematics and Statistics,Kashi University,Kashi 844000,China;School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China)
基金
supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China(2019D01A05)
supported by the NSFC(11571132)。