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Zbl 0978.35098
Hähner, Peter
On the uniqueness of the shape of a penetrable, anisotropic obstacle. (English)
[J] J. Comput. Appl. Math. 116, No.1, 167-180 (2000). ISSN 0377-0427

This paper studies the direct and inverse scattering problem for time harmonic waves by an inhomogeneous anisotropic medium. In the first part, the direct problem is studied by a variational approach with nonlocal boundary conditions involving the Dirichlet-Neumann operator. The main tool in the proof of uniqueness of the inverse problem consists of an investigation of the corresponding interior transmission problem. The author combines a contraction argument with the Fredholm theory to show existence and uniqueness of this problem. With the help of special solutions, the technique of Kirsch and Kress leads to uniqueness of the inverse problem.
[Andreas Kirsch (Karlsruhe)]

MSC 2000:: *35R30 Inverse problems for PDE
35Q60 PDE of electromagnetic theory and optics
78A46 Inverse scattering problems

Keywords: anisotropic obstacle; transmission problem; existence; uniqueness

Cited in: Zbl 1048.78008

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