Spectral properties of the Neumann-Poincare operator and cloaking by anomalous localized resonance for the elasto-static system

被引：32

作者：

Ando, Kazunori ^{[1
]}

Ji, Yong-Gwan ^{[2
]}

Kang, Hyeonbae ^{[2
]}

Kim, Kyoungsun ^{[3
]}

Yu, Sanghyeon ^{[4
]}

机构：

[1] Ehime Univ, Dept Elect & Elect Engn & Comp Sci, Matsuyama, Ehime 7908577, Japan

[2] Inha Univ, Dept Math, Incheon 22212, South Korea

[3] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[4] ETH, Seminar Appl Math, Ramistr 101, CH-8092 Zurich, Switzerland

来源：

EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2018年 / 29卷 / 02期

关键词：

Neumann-Poincare operator; Lame system; linear elasticity; spectrum; resonance; cloaking by anomalous localized resonance; LAYER POTENTIALS; ELASTOSTATICS; EQUATIONS; DOMAINS; BOUNDS;

D O I：

10.1017/S0956792517000080

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We first investigate spectral properties of the Neumann-Poincare (NP) operator for the Lame system of elasto-statics. We show that the elasto-static NP operator can be symmetrized in the same way as that for the Laplace operator. We then show that even if elasto-static NP operator is not compact even on smooth domains, it is polynomially compact and its spectrum on two-dimensional smooth domains consists of eigenvalues that accumulate to two different points determined by the Lame constants. We then derive explicitly eigenvalues and eigenfunctions on discs and ellipses. Using these resonances occurring at eigenvalues is considered. We also show on ellipses that cloaking by anomalous localized resonance takes place at accumulation points of eigenvalues.

引用

页码：189 / 225

页数：37