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Cakoni, Fioralba; Haddar, Houssem; Meng, Shixu

Boundary integral equations for the transmission eigenvalue problem for Maxwell’s equations. (English) Zbl 1332.35247

J. Integral Equations Appl. 27, No. 3, 375-406 (2015).
Summary: In this paper, we consider the transmission eigenvalue problem for Maxwell’s equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission eigenvalue problem as an equivalent homogeneous system of the boundary integral equation and, assuming that the contrast is constant near the boundary of the support of the inhomogeneity, we prove that the operator associated with this system is Fredholm of index zero and depends analytically on the wave number. Then we show the existence of wave numbers that are not transmission eigenvalues which by an application of the analytic Fredholm theory implies that the set of transmission eigenvalues is discrete with positive infinity as the only accumulation point.

Cited in 1 Review
Cited in 9 Documents

MSC:

35P25 Scattering theory for PDEs
35Q61 Maxwell equations
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory

Keywords:

transmission eigenvalue problem; inverse scattering; boundary integral equations; Maxwell’s equations
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Full Text: DOI Euclid

References:

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