THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM

被引：63

作者：

Cakoni, Fioralba ^{[1
]}

Colton, David ^{[1
]}

Gintides, Drossos ^{[2
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 06期

关键词：

interior transmission problem; transmission eigenvalues; inhomogeneous medium; inverse scattering; SPHERICALLY SYMMETRICAL SPEED; FAR-FIELD DATA; EXISTENCE; SOUND;

D O I：

10.1137/100793542

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the inverse problem of determining the spherically symmetric index of refraction n(r) from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction n(r) = n, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n sufficiently small and, for homogeneous media of general shape, determine a region in the complex plane where complex eigenvalues must lie.

引用

页码：2912 / 2921

页数：10

共 15 条

[1]

CAKONI F, 2007, INVERSE PROBL IMAG, V1, P13

[2] On the determination of Dirichlet or transmission eigenvalues from far field data [J].