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On an inverse electrodynamic problem. (Russian, English) Zbl 1109.35378

Zh. Vychisl. Mat. Mat. Fiz. 45, No. 11, 2052-2060 (2005); translation in Comput. Math. Math. Phys. 45, No. 11, 1973-1981 (2005).
The electrodynamic inverse problem of a conductivity determination for a metal sample from a measured resulting field outside of it and a known indirect field is considered. The solution ambiguity of an appropriate operator equation for magnetic and non-magnetic metals is established. For the case of non-magnetic materials the kernel of the integro-differential operator, included in the equation, is found.

MSC:

35R30 Inverse problems for PDEs
45Q05 Inverse problems for integral equations
35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory (general)
82D40 Statistical mechanics of magnetic materials
45K05 Integro-partial differential equations
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