TRANSMISSION EIGENVALUES

被引：130

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

[21] A duality between scattering poles and transmission eigenvalues in scattering theory [J].

Cakoni, Fioralba ;

Colton, David ;

Haddar, Houssem .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2020, 476 (2244)

[22] On the inverse scattering from anisotropic periodic layers and transmission eigenvalues [J].

Harris, Isaac ;

Nguyen, Dinh-Liem ;

Sands, Jonathan ;

Truong, Trung .

APPLICABLE ANALYSIS, 2022, 101 (08) :3065-3081

[23] A spectral projection method for transmission eigenvalues [J].

ZENG Fang ;

SUN JiGuang ;

XU LiWei .

ScienceChina(Mathematics), 2016, 59 (08) :1613-1622

[24] Transmission eigenvalues for degenerate and singular cases [J].

Serov, Valery ;

Sylvester, John .

INVERSE PROBLEMS, 2012, 28 (06)

[25] A spectral projection method for transmission eigenvalues [J].

Fang Zeng ;

JiGuang Sun ;

LiWei Xu .

Science China Mathematics, 2016, 59 :1613-1622

[26] Discreteness of interior transmission eigenvalues revisited [J].

Hoai-Minh Nguyen ;

Quoc-Hung Nguyen .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2017, 56 (02)

[27] TRANSMISSION EIGENVALUES FOR OPERATORS WITH CONSTANT COEFFICIENTS [J].

Hitrik, Michael ;

Krupchyk, Katsiaryna ;

Ola, Petri ;

Paivarinta, Lassi .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (06) :2965-2986

[28] The inverse spectral problem for transmission eigenvalues [J].

Cogar, Samuel ;

Colton, David ;

Leung, Yuk-J .

INVERSE PROBLEMS, 2017, 33 (05)

[29] A spectral projection method for transmission eigenvalues [J].

Zeng Fang ;

Sun JiGuang ;

Xu LiWei .

SCIENCE CHINA-MATHEMATICS, 2016, 59 (08) :1613-1622

[30] Recursive integral method for transmission eigenvalues [J].

Huang, Ruihao ;

Struthers, Allan A. ;

Sun, Jiguang ;

Zhang, Ruming .

JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 327 :830-840

← 1 2 3 4 5 →