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Summary: Identi cation of small amplitude perturbations in the
electromagnetic parameters from partial dynamic
boundary measurements
Habib Ammari
Abstract
We consider the inverse problem of reconstructing small amplitude perturbations
in the conductivity for the wave equation from partial (on part of the boundary) dy-
namic 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 appropri-
ate averaging of the partial dynamic boundary perturbations. This asymptotic formula
is generalized to the full time-dependent Maxwell's equations. Our formulae may be
expected to lead to very e ective computational identi cation algorithms, aimed at de-
termining electromagnetic parameters of an object based on partial dynamic boundary
measurements.
Key words. inverse problem, wave equation, Maxwell's equations, reconstruction,
electromagnetic coeÆcients, geometric control
2000 AMS subject classi cations. 35R30, 35B40, 35B37, 35L05
1 Introduction
The ultimate objective of the work described in this paper is to determine, most e ec-
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