THE ELECTROMAGNETIC INTERIOR TRANSMISSION PROBLEM FOR REGIONS WITH CAVITIES

被引：16

作者：

Cossonniere, Anne ^{[1
]}

Haddar, Houssem ^{[2
]}

机构：

[1] CERFACS, F-31057 Toulouse 01, France

[2] Ecole Polytech, CMAP, INRIA Saclay Ile France, Route Saclay, F-91128 Palaiseau, France

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2011年 / 43卷 / 04期

关键词：

interior transmission problem; inhomogeneous medium; transmission eigenvalues; REFRACTION; INDEX;

D O I：

10.1137/100813890

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the electromagnetic interior transmission problem in the case when the medium has cavities, i.e., regions in which the index of refraction is the same as in the host medium. We address the configuration where the electromagnetic permeability is constant while the electric permittivity is variable and may be anisotropic. In this case, using appropriate reformulation of the problem into a fourth order PDE, we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. Monotonicity properties of the first eigenvalue in terms of the permittivity and the size of the cavity are established.

引用

页码：1698 / 1715

页数：18

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