English
Related papers

Related papers: The anisotropic interior transmission eigenvalue p…

200 papers

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

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

The paper is devoted to the study of some properties of the first eigenvalue of the anisotropic $p$-Laplace operator with Robin boundary condition involving a function $\beta$ which in general is not constant. In particular we obtain sharp…

Analysis of PDEs · Mathematics 2018-03-28 Nunzia Gavitone , Leonardo Trani

In this work, we study the eigenvalue problem associated with the bidomain operator in an anisotropic heterogeneous domain composed of three subregions representing the left ventricle, the septum, and the right ventricle. The anisotropic…

Analysis of PDEs · Mathematics 2026-04-07 Raul Felipe-Sosa , Yofre H. García-Gómez

We study the location of the transmission eigenvalues in the isotropic case when the restrictions of the refraction indices on the boundary coincide. Under some natural conditions we show that there exist parabolic transmission…

Analysis of PDEs · Mathematics 2017-02-14 Georgi Vodev

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 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

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 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 determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using also some properties related to the associated \lq\lq…

Analysis of PDEs · Mathematics 2024-10-08 Gianpaolo Piscitelli

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 obtain parabolic transmission eigenvalue-free regions for both isotropic andanisotropic interior transmission problems with coefficients which are Lipschitznear the boundary

Analysis of PDEs · Mathematics 2023-03-31 Georgi Vodev

In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Two theorems on strong solvability and the…

Analysis of PDEs · Mathematics 2021-03-12 Abdumauvlen S. Berdyshev

In this paper we analyse a boundary value problem for the Laplace equation with a nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of size $\epsilon$. We show that the problem has solutions for…

Analysis of PDEs · Mathematics 2022-11-24 Riccardo Molinarolo

In this paper, we consider an interior transmission eigenvalue problem on two compact Riemannian manifolds with common smooth boundary. We suppose that a couple of these manifolds is equipped with locally anisotropic type Riemannian metric…

Spectral Theory · Mathematics 2017-03-14 Naotaka Shoji

The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrix have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them…

Analysis of PDEs · Mathematics 2012-10-24 Mihai Bostan

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

The unique determination of electrical conductivity is extensively studied for isotropic conductivity ever since Calderon's suggestion of the EIT (Electrical Impedance Tomography) problem. However, it is known that there are many…

Analysis of PDEs · Mathematics 2013-04-25 Kiwoon Kwon

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

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