The point source inverse back-scattering problem
The point source inverse back-scattering problem
复制标题
点源逆后向散射问题
DOI：
10.1090/conm/644/12784
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
G. Uhlmann
中科院分区：
文献类型：
--
作者：
Rakesh;G. Uhlmann
我们考虑的逆问题恢复的潜力，通过测量在一个点的响应，位于同一点的源，然后改变点的表面上的一个球体。这类似于反向散射问题。我们证明，如果两个具有相同数据的势的差的角导数由势的差的L^2范数控制，则它们必须相等。特别是，这表明径向势的反问题的单射性。
We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering problem. We show that if the angular derivatives of the difference of two potentials having the same data is controlled by the L^2 norm of the difference of the potentials they must be equal. In particular this shows injectivity of the inverse problem for radial potentials.