Related papers: Interior transmission eigenvalue problems on compa…
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.…
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…
In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete, if the electromagnetic parameters $\eps, \, \mu,…
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…
In this paper we prove some results on interior transmission eigenvalues. First, under rea- sonable assumptions, we prove that the spectrum is a discrete countable set and the generalized eigenfunctions spanned a dense space in the range of…
We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first…
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…
We show that the interior transmission eigenvalues are discrete by proving that the interior transmission operator has upper triangular compact resolvent, and that the spectrum of these operators share many of the properties of operators…
We study the high-frequency behavior of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use…
In this paper, we investigate two transmission eigenvalue problems associated with the scattering of a media with a coated boundary. In recent years, there has been a lot of interest in studying these eigenvalue problems. It can be shown…
For the complex interior transmission eigenvalues (ITE) we study for small $\theta > 0$ the counting function $$N(\theta, r) = #\{\lambda \in \C:\: \lambda \: {\rm is} \: {\rm (ITE)},\: |\lambda| \leq r, \: 0 \leq \arg \lambda \leq…
We consider a transmission problem for the Helmholtz equation across the boundary of an extension domain. A such boundary can be Lipschitz, fractal, or of varying Hausdorff dimension for instance. We generalise the notions of layer…
In this note we establish an expression for the Steklov spectrum of warped products in terms of auxiliary Steklov problems for drift Laplacians with weight induced by the warping factor. As an application, we show that a compact manifold…
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…
In this paper we extend the results in [16] to more general domains. More precisely, we obtain transmission eigenvalue-free regions for the interior transmission problem with one complex-valued refraction index, that is, with a damping term…
We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…
We study the localization of the interior transmission eigenvalues (ITEs) in the case when the domain is the unit ball $\{x \in {\mathbb R}^d:\: |x| \leq 1\}, \: d\geq 2,$ and the coefficients $c_j(x), \: j =1,2,$ and the indices of…
This paper develops a scattering theory for the asymmetric transport observed at interfaces separating two-dimensional topological insulators. Starting from the spectral decomposition of an unperturbed interface Hamiltonian, we present a…
In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…
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…