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 | References | Similar Articles | Additional Information

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.

**[1]**R. S. Beezley and R. J. Krueger,*An electromagnetic inverse problem for dispersive media*, J. Math. Phys.**26**(1985), no. 2, 317–325. MR**776500**, https://doi.org/10.1063/1.526661**[2]**J. P. Corones, R. J. Krueger, and V. H. Weston,*Some recent results in inverse scattering theory*, Inverse problems of acoustic and elastic waves (Ithaca, N.Y., 1984) SIAM, Philadelphia, PA, 1984, pp. 65–81. MR**804617****[3]**R. B. Guenther and J. W. Lee,*Partial Differential Equations of Mathematical Physics and Integral Equations*, Prentice-Hall, Englewood Cliffs, N. J., 1988**[4]**John David Jackson,*Classical electrodynamics*, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. MR**0436782****[5]**L. D. Landau and E. M. Lifschitz,*Lehrbuch der theoretischen Physik (“Landau-Lifschitz”). Band VIII*, 4th ed., Akademie-Verlag, Berlin, 1985 (German). Elektrodynamik der Kontinua. [Electrodynamics of continua]; Translated from the second Russian edition by S. L. Drechsler; Translation edited by Gerd Lehmann; With a foreword by P. Ziesche and Lehmann. MR**820721****[6]**I. Lerche,*Some singular, nonlinear, integral equations arising in physical problems*, Quart. Appl. Math.**44**(1986), no. 2, 319–326. MR**856186**, https://doi.org/10.1090/S0033-569X-1986-0856186-6**[7]**N. I. Muskhelishvili,*Singular integral equations*, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR**0355494**

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Additional Information

DOI:
https://doi.org/10.1090/qam/1106390

Article copyright:
© Copyright 1991
American Mathematical Society