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Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 4
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Original Articles

On the existence of transmission eigenvalues in an inhomogeneous medium

Fioralba Cakoni Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553, USACorrespondence[email protected]
&
Houssem Haddar INRIA Saclay Ile de France/CMAP Ecole Polytechnique, Route de Saclay, 91128, Palaiseau Cedex, France
Pages 475-493 | Received 24 Dec 2008, Accepted 28 Dec 2008, Published online: 16 Jun 2009

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I. Harris. (2021) Analysis of two transmission eigenvalue problems with a coated boundary condition. Applicable Analysis 100:9, pages 1996-2019.
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I. Harris & A. Kleefeld. (2020) The inverse scattering problem for a conductive boundary condition and transmission eigenvalues. Applicable Analysis 99:3, pages 508-529.
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O. Bondarenko, I. Harris & A. Kleefeld. (2017) The interior transmission eigenvalue problem for an inhomogeneous media with a conductive boundary. Applicable Analysis 96:1, pages 2-22.
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Kyle S. Hickmann. (2012) Interior transmission eigenvalue problem with refractive index having C2-transition to the background medium. Applicable Analysis 91:9, pages 1675-1690.
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Guozheng Yan & Mao Yao. (2011) On the Nonexistence of Transmission Eigenvalues for Regions with Cavities. Communications in Partial Differential Equations 36:8, pages 1510-1519.
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Articles from other publishers (84)

Jianli Xiang & Guozheng Yan. (2023) The interior transmission eigenvalue problem for an anisotropic medium by a partially coated boundary. Acta Mathematica Scientia 44:1, pages 339-354.
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Jing An, Ting Tan & Zhimin Zhang. (2023) A Novel Spectral Approximation and Error Estimation for Transmission Eigenvalues in Spherical Domains. Journal of Scientific Computing 96:2.
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Jian Meng, Gang Wang & Liquan Mei. (2023) Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes. IMA Journal of Numerical Analysis 43:3, pages 1685-1717.
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Martin Halla. (2023) Electromagnetic Steklov eigenvalues: existence and distribution in the self-adjoint case. Research in the Mathematical Sciences 10:2.
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Ting Tan, Waixiang Cao & Jing An. (2022) Spectral approximation based on a mixed scheme and its error estimates for transmission eigenvalue problems. Computers & Mathematics with Applications 111, pages 20-33.
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Wei-Chen Chang, Tiexiang Li, Wen-Wei Lin & Jenn-Nan Wang. (2021) Computation of the interior transmission eigenvalues for elastic scattering in an inhomogeneous medium containing an obstacle. Research in the Mathematical Sciences 8:3.
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Fioralba Cakoni, Pu-Zhao Kow & Jenn-Nan Wang. (2021) The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems & Imaging 15:3, pages 445.
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Shixian Ren, Ting Tan & Jing An. (2020) An efficient spectral-Galerkin approximation based on dimension reduction scheme for transmission eigenvalues in polar geometries. Computers & Mathematics with Applications 80:5, pages 940-955.
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Wei-Chen Chang, Wen-Wei Lin & Jenn-Nan Wang. (2020) Efficient methods of computing interior transmission eigenvalues for the elastic waves. Journal of Computational Physics 407, pages 109227.
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Yingxia Xi, Xia Ji & Shuo Zhang. (2020) A multi-level mixed element scheme of the two-dimensional Helmholtz transmission eigenvalue problem. IMA Journal of Numerical Analysis 40:1, pages 686-707.
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Hai Bi, Jiayu Han & Yidu Yang. (2018) Local and Parallel Finite Element Algorithms for the Transmission Eigenvalue Problem. Journal of Scientific Computing 78:1, pages 351-375.
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David Colton & Rainer KressDavid Colton & Rainer Kress. 2019. Inverse Acoustic and Electromagnetic Scattering Theory. Inverse Acoustic and Electromagnetic Scattering Theory 371 437 .
Hao Li & Yidu Yang. (2018) An adaptive C0IPG method for the Helmholtz transmission eigenvalue problem. Science China Mathematics 61:8, pages 1519-1542.
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Jing An & Zhimin Zhang. (2017) An Efficient Spectral-Galerkin Approximation and Error Analysis for Maxwell Transmission Eigenvalue Problems in Spherical Geometries. Journal of Scientific Computing 75:1, pages 157-181.
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Meiman SUN & Guozheng YAN. (2018) Discreteness of the exterior transmission eigenvalues. Acta Mathematica Scientia 38:1, pages 110-124.
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Yidu Yang, Hai Bi, Hao Li & Jiayu Han. (2017) A method and its error estimates for the Helmholtz transmission eigenvalue problem . Journal of Computational and Applied Mathematics 326, pages 71-86.
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Xiaofei Li, Jingzhi Li, Hongyu Liu & Yuliang Wang. (2017) Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking. IMA Journal of Applied Mathematics 82:5, pages 1013-1042.
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Tiexiang Li, Tsung-Ming Huang, Wen-Wei Lin & Jenn-Nan Wang. (2017) An efficient numerical algorithm for computing densely distributed positive interior transmission eigenvalues. Inverse Problems 33:3, pages 035009.
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Jiayu Han, Yidu Yang & Hai Bi. (2017) A new multigrid finite element method for the transmission eigenvalue problems. Applied Mathematics and Computation 292, pages 96-106.
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Jing An. (2016) A Legendre–Galerkin spectral approximation and estimation of the index of refraction for transmission eigenvalues. Applied Numerical Mathematics 108, pages 171-184.
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TongXing Li & JiJun Liu. (2015) Transmission eigenvalue problem for inhomogeneous absorbing media with mixed boundary condition. Science China Mathematics 59:6, pages 1081-1094.
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Stefan Peters & Andreas Kleefeld. (2016) Numerical computations of interior transmission eigenvalues for scattering objects with cavities. Inverse Problems 32:4, pages 045001.
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Xia Ji, Hongrui Geng, Jiguang Sun & Liwei Xu. (2016) C 0 IPG for a Fourth Order Eigenvalue Problem . Communications in Computational Physics 19:2, pages 393-410.
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Yidu Yang, Hai Bi, Hao Li & Jiayu Han. (2016) Mixed Methods for the Helmholtz Transmission Eigenvalues. SIAM Journal on Scientific Computing 38:3, pages A1383-A1403.
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Jing An & Jie Shen. (2013) A Spectral-Element Method for Transmission Eigenvalue Problems. Journal of Scientific Computing 57:3, pages 670-688.
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Xia Ji, Jiguang Sun & Tiara Turner. (2012) Algorithm 922. ACM Transactions on Mathematical Software 38:4, pages 1-8.
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T. Turner, Jiguang Sun & Fengshan Liu. (2012) On electromagnetic transmission eigenvalues. On electromagnetic transmission eigenvalues.
Lucas Chesnel. (2012) Interior transmission eigenvalue problem for Maxwell's equations: the T -coercivity as an alternative approach . Inverse Problems 28:6, pages 065005.
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Fioralba Cakoni, David Colton & Houssem Haddar. (2012) The interior transmission eigenvalue problem for absorbing media. Inverse Problems 28:4, pages 045005.
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Andreas Kirsch & Albert Ruiz. (2012) The Factorization Method for an inverse fluid-solid interaction scattering problem. Inverse Problems & Imaging 6:4, pages 681-695.
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Kyoungsun Kim, Gen Nakamura & Mourad Sini. (2012) The Green function of the interior transmission problem and its applications. Inverse Problems & Imaging 6:3, pages 487-521.
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Tuncay Aktosun, Drossos Gintides & Vassilis G Papanicolaou. (2011) The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Problems 27:11, pages 115004.
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