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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R. B. Guenther and J. W. Lee, Partial Differential Equations of Mathematical Physics and Integral Equations, Prentice-Hall, Englewood Cliffs, N. J., 1988
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R. S. Beezley and R. J. Krueger, An electromagnetic inverse problem for dispersive media, J. Math. Phys. 26, 317–325 (1985)
J. P. Corones, R. J. Krueger, and V. H. Weston, Some recent results in inverse scattering theory, Inverse Problems of Acoustic and Elastic Waves (ed. by F. Santosa, Y.-H. Pao, W. W. Symes, and Ch. Holland), SIAM, Philadelphia, 65–81, 1984
R. B. Guenther and J. W. Lee, Partial Differential Equations of Mathematical Physics and Integral Equations, Prentice-Hall, Englewood Cliffs, N. J., 1988
J. D. Jackson, Classical Electrodynamics, Wiley, New York, 1975
L. D. Landau and E. M. Lifschitz, Lehrbuch der theoretischen Physik, Vol. VIII, Elektrodynamik der Kontinua, 4th ed., Akademie-Verlag, Berlin, 1985
I. Lerche, Some singular, nonlinear integral equations arising in physical problems, Quart. Appl. Math. 44, 319–326 (1986)
N. I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen, 1953
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Article copyright:
© Copyright 1991
American Mathematical Society