The Inverse Scattering Problem for a Penetrable Cavity with Internal Measurements
The Inverse Scattering Problem for a Penetrable Cavity with Internal Measurements
复制标题
DOI：
10.1090/conm/615/12246
复制
发表时间：
2013
影响因子：
--
通讯作者：
F. Cakoni;D. Colton;S. Meng
中科院分区：
文献类型：
--
作者：
F. Cakoni;D. Colton;S. Meng
我们考虑由致密支撑的可穿透非均匀介质所包围的空腔的逆散射问题，并试图通过在空腔内部曲线或表面上的内部测量来确定空腔的形状。我们证明了唯一性，并建立了一种确定空腔形状的线性采样方法。在我们的分析中起中心作用的是一个不寻常的非自伴随特征值问题，我们称之为外部传输特征值问题。献给冈瑟·乌尔曼，在他60岁生日之际
We consider the inverse scattering problem for a cavity that is bounded by a penetrable inhomogeneous medium of compact support and seek to determine the shape of the cavity from internal measurements on a curve or surface inside the cavity. We prove uniqueness and establish a linear sampling method for determining the shape of the cavity. A central role in our analysis is played by an unusual non-selfadjoint eigenvalue problem which we call the exterior transmission eigenvalue problem. Dedicated to Gunther Uhlmann on the occasion of his 60th birthday