Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On an electromagnetic inverse problem for dispersive media


Author: L. von Wolfersdorf
Journal: Quart. Appl. Math. 49 (1991), 237-246
MSC: Primary 35A30; Secondary 35Q60, 78A40
DOI: https://doi.org/10.1090/qam/1106390
MathSciNet review: MR1106390
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Abstract: Recently, R. S. Beezley and R. J. Krueger [1] (see also [2]) and I. Lerche [6] considered some electromagnetic inverse problems for dispersive media, where the constitutive relation between the displacement field and the electric field in a homogeneous, isotropic, dielectric, dispersive medium is determined from measurements on monochromatic electromagnetic plane waves within the medium. For this aim Beezley and Krueger used the reflection behavior of the plane waves in the time domain, whereas Lerche utilized the absorption behavior of the waves in the frequency domain stressing the fact that decrement measurements are relatively easy to perform compared to phase measurements. He reduced the corresponding inverse problem for the whole space to a nonlinear Riemann-Hilbert problem for a holomorphic function in the upper half-plane and (not quite exactly) to an equivalent nonlinear singular integral equation which he solved in a linear approximation.


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DOI: https://doi.org/10.1090/qam/1106390
Article copyright: © Copyright 1991 American Mathematical Society


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