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In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. First, we discuss the inverse conductivity problem of reconstructing the conductivity parameter from scattering…

Analysis of PDEs · Mathematics 2017-12-12 Isaac Harris , Andreas Kleefeld

We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…

Analysis of PDEs · Mathematics 2020-04-15 Isaac Harris , Andreas Kleefeld

In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer.…

Analysis of PDEs · Mathematics 2022-09-16 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld , Nikolaos Pallikarakis

In this paper, we investigate the interior transmission eigenvalue problem for an inhomogeneous media with conductive boundary conditions. We prove the discreteness and existence of the transmission eigenvalues. We also investigate the…

Analysis of PDEs · Mathematics 2016-10-31 Oleksandr Bondarenko , Isaac Harris , Andreas Kleefeld

In this paper, we study the transmission eigenvalue problem for an anisotropic material with a conductive boundary. We prove that the transmission eigenvalues for this problem exist and are at most a discrete set. We also study the…

Analysis of PDEs · Mathematics 2023-11-02 Victor Hughes , Isaac Harris , Jiguang Sun

In this paper, we provide an analytical study of the transmission eigenvalue problem in the context of biharmonic scattering with a penetrable obstacle. We will assume that the underlying physical model is given by an infinite elastic…

Analysis of PDEs · Mathematics 2025-10-10 Rafael Ceja Ayala , Isaac Harris , Andreas Kleefeld

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 transmission eigenfunctions are the interior resonant…

Analysis of PDEs · Mathematics 2023-04-24 Yat Tin Chow , Youjun Deng , Hongyu Liu , Mahesh Sunkula

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

In this paper, we present a Spectral-Galerkin Method to approximate the zero-index transmission eigenvalues with a conductive boundary condition. This is a new eigenvalue problem derived from the scalar inverse scattering problem for an…

Numerical Analysis · Mathematics 2020-02-27 Isaac Harris

This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from…

Analysis of PDEs · Mathematics 2020-01-10 Isaac Harris , Dinh-Liem Nguyen , Jonathan Sands , Trung Truong

The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…

Spectral Theory · Mathematics 2016-10-06 Tuncay Aktosun , Vassilis G. Papanicolaou

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is posted as a system of two second order partial differential…

Numerical Analysis · Mathematics 2020-01-16 Bo Gong , Jiguang Sun , Tiara Turner , Chunxiong Zheng

In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff--Love infinite plate problem.…

Analysis of PDEs · Mathematics 2025-02-04 Isaac Harris , Heejin Lee , Andreas Kleefeld

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 the direct and inverse scattering problems in many…

Analysis of PDEs · Mathematics 2020-12-07 Hongyu Liu

We consider the direct and inverse scattering problem for a penetrable, isotropic obstacle with a second-order Robin boundary condition, which asymptotically models the delamination of the boundary of the scatterer. We develop a direct…

Analysis of PDEs · Mathematics 2026-01-22 Govanni Granados , Isaac Harris , Andreas Kleefeld

The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…

Analysis of PDEs · Mathematics 2018-05-21 Samuel Cogar , David Colton , Peter Monk

In this paper, we study the so-called clamped transmission eigenvalue problem. This is a new transmission eigenvalue problem that is derived from the scattering of an impenetrable clamped obstacle in a thin elastic plate. The scattering…

Analysis of PDEs · Mathematics 2025-11-21 Isaac Harris , Andreas Kleefeld , Heejin Lee

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

A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce…

Analysis of PDEs · Mathematics 2020-10-13 Samuel Cogar , Peter Monk
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