相关论文: Inside-outside duality with artificial backgrounds

For the direct problem, we give the asymptotic distribution of the (real and non-real) transmission eigenvalues for the Schrodinger operator on the half line. For the inverse problem, we prove that the potential can be uniquely determined…

An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the…

We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features…

In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.

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…

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…

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…

This paper presents a new approach to the two-interval Sturm-Liouville eigenfunction expansions, based essentially on the method of integral equations. We consider the Sturm-Liouville problem together with two supplementary transmission…

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…

In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…

In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…

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…

A concrete formulation of the Lehmann-Maehly-Goerisch method for semi-definite self-adjoint operators with compact resolvent is considered. Precise rates of convergence are determined in terms of how well the trial spaces capture the…

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…

In this paper, we discuss a virtual element approximation for the modified transmission eigenvalue problem in inverse scattering for natural materials. In this case, due to the positive artificial diffusivity parameter in the considered…

We consider an inverse spectral theory in a domain with the cavity that is bounded by a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the solutions inside and outside the cavity. The ODE system is connected…

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…

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…

The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…

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…