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On uniqueness of obstacles and boundary conditions from restricted dynamical and scattering data
Isakov, Victor
Isakov, Victor
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2008-02
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Article
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Inverse Problems,Inverse Scattering Problems
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Isakov, Victor. 2007. On uniqueness of obstacles and boundary conditions from restricted dynamical and scattering data. Inverse Problems and Imaging.
Abstract
We show uniqueness of a (time independent) domain D and of an
impedance type boundary condition from either dynamical or scattering data
at many frequencies. We assume that the additonal boundary (scattering) data
are given for one set of boundary data or for one incident direction. In case
of general domain and finite (sharp) observation time we assume Neumann
boundary condition on ∂D and for polygonal D we can handle more general
case. If the data are available for all times we show uniqueness of the most general
impedance boundary condition by using continuation of the corresponding
scattering data into complex domain and modifying the Schiffer’s argument.
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American Institute of Mathematical Sciences
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Inverse Problems and Imaging
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1930-8337
1930-8345
1930-8345