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Zbl 0728.35148
Isakov, Victor
On uniqueness in the inverse transmission scattering problem.
(English)
[J] Commun. Partial Differ. Equations 15, No.11, 1565-1587 (1990). ISSN 0360-5302; ISSN 1532-4133/e

In this paper uniqueness results are proved for the inverse scattering problems where the unknown scatterer D is a bounded open set and some coefficients of an elliptic equation are unknown as well. Let $D\sp i$ be the bounded open set in $R\sp n$, $D\sp e=R\sp n\setminus D\sp i$, $u=u\sp e$ in $D\sp e$, $u=u\sp i$ in $D\sp i$, $\chi$ (D) the characteristic function of D, $a=1+(\mu -1)\chi (D)$, $c=1+(\rho -1)\chi (D)$. Further, let u be a solution of $div(a\nabla u)+k\sp 2cu=0$, satisfying $u\sp i=u\sp e$, $\partial u\sp e/\partial N=\mu \partial u\sp i/\partial N$ on $\partial D$, $u\sp e(x)=\exp (ix\cdot \xi +u\sp{e\sb 0}(x)$, $\vert \xi \vert =k$, $r\sp{(n-1)/2}(\partial u\sp{e\sb 0}/\partial r-iku\sp{e\sb 0})\to 0$ for $r\to \infty$. The author applies ideas of Nachman, Sylvester, Uhlmann and own results for this special problem under consideration.
[G.Anger (Berlin)]
MSC 2000:
*35R30 Inverse problems for PDE
35P25 Scattering theory (PDE)
35J10 Schroedinger operator
78A40 Waves and radiation

Keywords: uniqueness results; inverse scattering problems

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