Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)

  • [1] R. S. Beezley and R. J. Krueger, An electromagnetic inverse problem for dispersive media, J. Math. Phys. 26, 317-325 (1985) MR 776500
  • [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 (ed. by F. Santosa, Y.-H. Pao, W. W. Symes, and Ch. Holland), SIAM, Philadelphia, 65-81, 1984 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] J. D. Jackson, Classical Electrodynamics, Wiley, New York, 1975 MR 0436782
  • [5] L. D. Landau and E. M. Lifschitz, Lehrbuch der theoretischen Physik, Vol. VIII, Elektrodynamik der Kontinua, 4th ed., Akademie-Verlag, Berlin, 1985 MR 820721
  • [6] I. Lerche, Some singular, nonlinear integral equations arising in physical problems, Quart. Appl. Math. 44, 319-326 (1986) MR 856186
  • [7] N. I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen, 1953 MR 0355494

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35A30, 35Q60, 78A40

Retrieve articles in all journals with MSC: 35A30, 35Q60, 78A40

Additional Information

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

American Mathematical Society