TRANSMISSION EIGENVALUES FOR INHOMOGENEOUS MEDIA CONTAINING OBSTACLES

被引：19
作者：
Cakoni, Fioralba [1 ]
Cossonniere, Anne [2 ]
Haddar, Houssem [3 ]
机构：
[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
[2] CERFACS, F-31057 Toulouse 01, France
[3] CMAP Ecole Polytech, INRIA Saclay Ile France, F-91128 Palaiseau, France
来源：
INVERSE PROBLEMS AND IMAGING | 2012年 / 6卷 / 03期
关键词：
Interior transmission problem; transmission eigenvalues; inhomogeneous medium; inverse scattering problem; REFRACTION; REGIONS; BOUNDS; INDEX;
D O I：
10.3934/ipi.2012.6.373
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the interior transmission problem corresponding to the inverse scattering by an inhomogeneous (possibly anisotropic) media in which an impenetrable obstacle with Dirichlet boundary conditions is embedded. Our main focus is to understand the associated eigenvalue problem, more specifically to prove that the transmission eigenvalues form a discrete set and show that they exist. The presence of Dirichlet obstacle brings new difficulties to already complicated situation dealing with a non-selfadjoint eigenvalue problem. In this paper, we employ a variety of variational techniques under various assumptions on the index of refraction as well as the size of the Dirichlet obstacle.
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收藏
页码：373 / 398
页数：26
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