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On the reconstruction of a metric from external electromagnetic measurements. (English. Russian original) Zbl 1048.35132

Dokl. Math. 61, No. 3, 353-356 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 372, No. 3, 298-300 (2000).
From the text: We develop an approach to inverse problems (IPs) that makes use of their relationship to boundary control theory (the BC-method. A dynamic inverse problem for the Maxwell system is considered in a bounded domain of a three-dimensional curved space. The domain is prospected by boundary sources of electromagnetic waves. The waves scattered by inhomogeneities of the metric are detected on the same boundary. The problem is to recover the metric from these measurements. The procedure proposed for solving the IP is time-optimal; i.e., the metric in the near-boundary subdomain of optical thickness \(T\) is recovered from measurements at time \(0<t<2T\). We restrict our consideration to a subdomain covered by a regular system of semigeodesic coordinates with its base placed on the boundary. Among the well-known results in this area, we mention uniqueness theorems for the Maxwell system in the frequency domain.

MSC:

35R30 Inverse problems for PDEs
35B37 PDE in connection with control problems (MSC2000)
35Q60 PDEs in connection with optics and electromagnetic theory
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
93C20 Control/observation systems governed by partial differential equations
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