TRANSMISSION EIGENVALUES

被引：128

作者：

Paivarinta, Lassi ^{[1
]}

Sylvester, John ^{[2
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, Helsinki, Finland

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2008年 / 40卷 / 02期

基金：

芬兰科学院;

关键词：

inverse scattering; Helmholtz equation; inverse problems; transmission eigenvalues;

D O I：

10.1137/070697525

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The scattering of a time-harmonic plane wave in an inhomogeneous medium is modeled by the scattering problem for the Helmholtz equation. A transmission eigenvalue is a wavenumber at which the scattering operator has a nontrivial kernel or cokernel. Because many sampling methods for locating scatterers succeed only at wavenumbers that are not transmission eigenvalues, they have been studied for some time. Nevertheless, the existence of transmission eigenvalues has previously been proved only for radial scatterers. In this paper, we prove existence for scatterers without radial symmetry.

引用

页码：738 / 753

页数：16

共 50 条

[31] Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators [J].

Ma, Yunyun ;

Ma, Fuming ;

Guo, Yukun ;

Li, Jingzhi .

CSIAM TRANSACTIONS ON APPLIED MATHEMATICS, 2023, 4 (02) :306-324

[32] DISCRETENESS OF TRANSMISSION EIGENVALUES FOR HIGHER-ORDER MAIN TERMS AND PERTURBATIONS [J].

Garcia, Andoni ;

Vesalainen, Esa V. ;

Zubeldia, Miren .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2016, 48 (04) :2382-2398

[33] CONTINUOUS DEPENDENCE OF THE TRANSMISSION EIGENVALUES IN ONE DIMENSION [J].

Zhang, Yalin ;

Shi, Guoliang .

INVERSE PROBLEMS AND IMAGING, 2015, 9 (01) :273-287

[34] THE ASYMPTOTIC OF TRANSMISSION EIGENVALUES FOR A DOMAIN WITH A THIN COATING [J].

Boujlida, H. ;

Haddar, H. ;

Khenissi, M. .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2018, 78 (05) :2348-2369

[35] A numerical method to compute interior transmission eigenvalues [J].

Kleefeld, Andreas .

INVERSE PROBLEMS, 2013, 29 (10)

[36] Modified transmission eigenvalues in inverse scattering theory [J].

Cogar, S. ;

Colton, D. ;

Meng, S. ;

Monk, P. .

INVERSE PROBLEMS, 2017, 33 (12)

[37] TRANSMISSION EIGENVALUES FOR INHOMOGENEOUS MEDIA CONTAINING OBSTACLES [J].

Cakoni, Fioralba ;

Cossonniere, Anne ;

Haddar, Houssem .

INVERSE PROBLEMS AND IMAGING, 2012, 6 (03) :373-398

[38] Asymptotic expansion of transmission eigenvalues for anisotropic thin layers [J].

Boujlida, H. ;

Haddar, H. ;

Khenissi, M. .

APPLICABLE ANALYSIS, 2024, 103 (02) :393-414

[39] FINITE ELEMENT METHODS FOR MAXWELL'S TRANSMISSION EIGENVALUES [J].

Monk, Peter ;

Sun, Jiguang .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (03) :B247-B264

[40] Reconstruction of modified transmission eigenvalues using Cauchy data [J].

Liu, Juan ;

Liu, Yanfang ;

Sun, Jiguang .

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2023, 31 (06) :905-919

← 1 2 3 4 5 →