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arXiv · 1707.04815

The Spectral Analysis of the Interior Transmission Eigenvalue Problem for Maxwell's Equations

Houssem Haddar·Shixu Meng
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Abstract

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that has fixed sign (only) in a neighborhood of the boundary. We study this problem in the framework of semiclassical analysis and relate the transmission eigenvalues to the spectrum of a Hilbert-Schmidt operator. Under the additional assumption that the contrast is constant in a neighborhood of the boundary, we prove that the set of transmission eigenvalues is discrete, infinite and without finite accumulation points. A notion of generalized eigenfunctions is introduced and a denseness result is obtained in an appropriate solution space.

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Houssem Haddar, Shixu Meng. 2017-07-16. The Spectral Analysis of the Interior Transmission Eigenvalue Problem for Maxwell's Equations. https://doi.org/10.1016/j.matpur.2018.10.004

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