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Identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements. (English) Zbl 1082.78006

We consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial (on part of the boundary) dynamic boundary measurements. Through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse Fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations. This asymptotic formula is generalized to the full time-dependent Maxwell equations. Our formulae may be expected to lead to very effective computational identification algorithms, aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements.

MSC:

78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35L20 Initial-boundary value problems for second-order hyperbolic equations
35R30 Inverse problems for PDEs
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