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On inverse scattering by screens. (English) Zbl 0901.35106
The authors prove uniqueness of a (not closed) surface $$\Gamma\in C^1$$ (screen) in $$\mathbb{R}^3$$ and of the acoustic impedance coefficient $$Z(x)$$ (Re $$Z\geq 0)$$ when the scattering amplitude $${\mathcal A}$$ is given at one (real) frequency $$k$$ for all incident directions $$d$$ and all directions $$\sigma$$ of the receiver. In more detail, $(\Delta+ k^2)u=0\quad \text{in } \mathbb{R}^3 \setminus \Gamma,\quad \partial_\nu u+ iZku= 0\quad\text{on } \Gamma,$
$u(x)= e^{ikd \cdot x} +e^{ik | x|}/ | x| {\mathcal A} (\sigma,d;k) +O(1/ | x|^2).$ In proofs they modify the method of singular solutions due to Kirsch, Kress and the reviewer. The authors present a quite efficient quasi-Newton-type numerical scheme for the reconstruction of the plane $$\Gamma$$.
Reviewer: V.Isakov (Wichita)

##### MSC:
 35R30 Inverse problems for PDEs 35P25 Scattering theory for PDEs 76Q05 Hydro- and aero-acoustics
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