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This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If…

Analysis of PDEs · Mathematics 2022-02-21 Plamen Stefanov , Yimin Zhong

We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…

Analysis of PDEs · Mathematics 2023-04-05 I-Kun Chen , Daisuke Kawagoe

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

In this paper, we investigate the sampling analysis associated with discontinuous Sturm-Liouville problem which has transmission conditions at two points of discontinuity also contains an eigenparameter in a boundary condition and two…

Classical Analysis and ODEs · Mathematics 2015-02-27 Fatma Hira , Nihat Altinisik

The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…

Spectral Theory · Mathematics 2018-05-22 Tuncay Aktosun , Vassilis G. Papanicolaou

The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$, $n=2,3$. Second, we…

Analysis of PDEs · Mathematics 2025-04-23 Huaian Diao , Xiaoxu Fei , Hongyu Liu

We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…

Analysis of PDEs · Mathematics 2015-05-14 Fernando Cardoso , Georgi Vodev

A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…

Spectral Theory · Mathematics 2021-11-01 Natalia P. Bondarenko , Vjacheslav A. Yurko

This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp…

Analysis of PDEs · Mathematics 2026-03-24 Yan Jiang , Hongyu Liu , Kai Zhang , Haoran Zheng

Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and…

Optics · Physics 2015-09-30 Liyi Zhao , Chushun Tian , Yury P. Bliokh , Valentin Freilikher

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

We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…

Exactly Solvable and Integrable Systems · Physics 2015-05-13 Gino Biondini , Guenbo Hwang

This work deals with the interior transmission eigenvalue problem: $y'' + {k^2}\eta \left( r \right)y = 0$ with boundary conditions ${y\left( 0 \right) = 0 = y'\left( 1 \right)\frac{{\sin k}}{k} - y\left( 1 \right)\cos k},$ where the…

Spectral Theory · Mathematics 2019-10-01 Xiao-Chuan Xu , Chuan-Fu Yang , Sergey A. Buterin , Vjacheslav A. Yurko

Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…

Analysis of PDEs · Mathematics 2013-05-07 Jiaqing Yang , Bo Zhang

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

In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary condition. We will assume that the corresponding far--field pattern or Cauchy data is either known or measured. The…

Analysis of PDEs · Mathematics 2025-01-10 Isaac Harris , Victor Hughes , Andreas Kleefeld

In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…

Analysis of PDEs · Mathematics 2021-04-21 Isaac Harris

In this work a discontinuous boundary-value problem with retarded argument which contains spectral parameter in the transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues…

Classical Analysis and ODEs · Mathematics 2015-06-12 Erdoğan Şen , Azad Bayramov

We consider the anisotropic interior transmission problem with one complex-valued refraction index. Under the condition that all geodesics reach the boundary in a finite time, we obtain large regions near the real axis free of transmission…

Analysis of PDEs · Mathematics 2024-03-06 Georgi Vodev

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