English
Related papers

Related papers: Analysis of the transmission eigenvalue problem fo…

200 papers

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…

Analysis of PDEs · Mathematics 2022-01-31 Michael Levitin , Peter Monk , Virginia Selgas

In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which…

Numerical Analysis · Mathematics 2016-08-24 Fang Zeng , Jiguang Sun , Liwei Xu

We study the propagation of elastic waves in the time-harmonic regime in a waveguide which is unbounded in one direction and bounded in the two other (transverse) directions. We assume that the waveguide is thin in one of these transverse…

Analysis of PDEs · Mathematics 2025-10-13 Laurent Bourgeois , Lucas Chesnel , Sonia Fliss

We are interested in a time harmonic acoustic problem in a waveguide with locally perturbed sound hard walls. We consider a setting where an observer generates incident plane waves at $-\infty$ and probes the resulting scattered field at…

Analysis of PDEs · Mathematics 2017-09-19 Anne-Sophie Bonnet-Ben Dhia , Lucas Chesnel , Sergei A. Nazarov

In this paper, we study the Helmholtz transmission eigenvalue problem for inhomogeneous anisotropic media with the index of refraction $n(x)\equiv 1$ in two and three dimension. Starting with a nonlinear fourth order formulation established…

Numerical Analysis · Mathematics 2023-04-26 Qing Liu , Tiexiang Li , Shuo Zhang

The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…

Mathematical Physics · Physics 2019-10-23 P. Zhevandrov , A. Merzon , M. I. Romero Rodríguez , J. E. de la Paz Méndez

We consider the interior transmission problem associated with the scattering by an inhomogeneous (possibly anisotropic) highly oscillating periodic media. We show that, under appropriate assumptions, the solution of the interior…

Analysis of PDEs · Mathematics 2015-10-12 Fioralba Cakoni , Houssem Haddar , Isaac Harris

This paper is concerned with the invisibility cloaking in acoustic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. It is shown that an…

Analysis of PDEs · Mathematics 2016-04-20 Xia Ji , Hongyu Liu

The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In this paper, we study the transmission eigenvalue problem for…

Numerical Analysis · Mathematics 2022-12-23 Shixi Wang , Hai Bi , Yidu Yang

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one…

Analysis of PDEs · Mathematics 2016-10-25 Hoai-Minh Nguyen , Quoc Hung Nguyen

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…

Mathematical Physics · Physics 2010-11-09 Evgeny Lakshtanov , Boris Vainberg

We study 4 problems in the area of scattering of time harmonic acoustic or electromagnetic waves by unbounded rough surfaces/inhomogeneous layers. Specifically we study: i) a boundary value problem (BVP) for the Helmholtz equation, in both…

Analysis of PDEs · Mathematics 2019-04-09 Thomas Baden-Riess

Scattering resonances arise in wave phenomena and play an important role in many applications. While extensive theoretical studies have been conducted, effective numerical computation remains limited, and most existing methods suffer from…

Numerical Analysis · Mathematics 2026-04-17 Bo Gong , Jiguang Sun

We analyze scattering in a system of two (distinguishable) particles moving on the half-line $\overline{\rz}_+$ under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions…

Mathematical Physics · Physics 2018-11-14 Sebastian Egger , Joachim Kerner

We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity…

Optics · Physics 2022-04-27 N. A. Vanyushkin , A. H. Gevorgyan , S. S. Golik

A recent area of interest is the development and study of eigenvalue problems arising in scattering theory that may provide potential target signatures for use in nondestructive testing of materials. We consider a generalization of the…

Analysis of PDEs · Mathematics 2020-07-01 Samuel Cogar

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that has fixed sign (only) in a neighborhood of the boundary. We…

Analysis of PDEs · Mathematics 2021-04-05 Houssem Haddar , Shixu Meng

We investigate the anharmonic phonon scattering across a weakly interacting interface by developing a quantum mechanics-based theory. We find that the contribution from anharmonic three-phonon scatterings to interfacial thermal conductance…

Mesoscale and Nanoscale Physics · Physics 2022-02-23 Hangbo Zhou , Gang Zhang , Jian-Sheng Wang , Yong-Wei Zhang

The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint…

Numerical Analysis · Mathematics 2016-06-29 Yidu Yang , Jiayu Han , Hai Bi

We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…

Spectral Theory · Mathematics 2025-08-18 Lung-Hui Chen