On local and global structures of transmission eigenfunctions and beyond
H Liu - Journal of Inverse and Ill-posed Problems, 2022 - degruyter.com
The (interior) transmission eigenvalue problems are a type of non-elliptic, non-selfadjoint
and nonlinear spectral problems that arise in the theory of wave scattering. They connect to …
and nonlinear spectral problems that arise in the theory of wave scattering. They connect to …
On vanishing and localizing of transmission eigenfunctions near singular points: a numerical study
This paper is concerned with the intrinsic geometric structure of interior transmission
eigenfunctions arising in wave scattering theory. We numerically show that the …
eigenfunctions arising in wave scattering theory. We numerically show that the …
Surface concentration of transmission eigenfunctions
The transmission eigenvalue problem is a type of non-elliptic and non-selfadjoint spectral
problem that arises in the wave scattering theory when invisibility/transparency occurs. The …
problem that arises in the wave scattering theory when invisibility/transparency occurs. The …
On vanishing and localizing around corners of electromagnetic transmission resonances
We are concerned with the geometric properties of the transmission resonance in
electromagnetic scattering. The transmission eigenvalue problem is a type of non-elliptic …
electromagnetic scattering. The transmission eigenvalue problem is a type of non-elliptic …
A novel method for solving the inverse spectral problem with the incomplete data
P Meng, Z Xu, X Wang, W Yin, H Liu - Journal of Computational and …, 2025 - Elsevier
This paper is concerned with an inverse spectral problem of the Dirichlet boundary in a
bounded region. We develop a novel method for determing the unknow objects by using a …
bounded region. We develop a novel method for determing the unknow objects by using a …
Conformal map** Coordinates Physics-Informed Neural Networks (CoCo-PINNs): learning neural networks for designing neutral inclusions
We focus on designing and solving the neutral inclusion problem via neural networks. The
neutral inclusion problem has a long history in the theory of composite materials, and it is …
neutral inclusion problem has a long history in the theory of composite materials, and it is …
Electromagnetic interior transmission eigenvalue problem for inhomogeneous media containing obstacles and its applications to near cloaking
This article is concerned with the invisibility cloaking in electromagnetic wave scattering from
a new perspective. We are especially interested in achieving the invisibility cloaking by …
a new perspective. We are especially interested in achieving the invisibility cloaking by …
[BOOK][B] Spectral Theory of Localized Resonances and Applications
Y Deng, H Liu - 2024 - Springer
This book is devoted to the spectral theory of localized resonances including surface
plasmon/polariton resonances, atypical resonances, anomalous localized resonances and …
plasmon/polariton resonances, atypical resonances, anomalous localized resonances and …
Construction of inclusions with vanishing generalized polarization tensors by imperfect interfaces
We investigate the problem of planar conductivity inclusion with imperfect interface
conditions. We assume that the inclusion is simply connected. The presence of the inclusion …
conditions. We assume that the inclusion is simply connected. The presence of the inclusion …
Interior Transmission Resonance
Y Deng, H Liu - Spectral Theory of Localized Resonances and …, 2024 - Springer
In this chapter, we consider the interior transmission eigenvalue problem. Our focus is on
justifying that the transmission eigenfunctions form a certain interior resonant modes. In fact …
justifying that the transmission eigenfunctions form a certain interior resonant modes. In fact …