Related papers: On the transmission eigenvalues for scattering by …
This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…
In this paper, we consider an interior transmission eigenvalue (ITE) problem on some compact $C^{\infty }$-Riemannian manifolds with a common smooth boundary. In particular, these manifolds may have different topologies, but we impose some…
We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in…
In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to…
A particular mix of integral equations and discretization techniques is suggested for the solution of a planar Helmholtz transmission problem with relevance to the study of surface plasmon waves. The transmission problem describes the…
In this paper, we consider the problem of the scattering of in-plane waves at an interface between a homogeneous medium and a metamaterial. The relevant eigenmodes in the two regions are calculated by solving a recently described non…
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…
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…
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…
This paper concerns an inverse elastic scattering problem which is to determine the location and the shape of a rigid obstacle from the phased or phaseless far-field data for a single incident plane wave. By introducing the Helmholtz…
We study the inverse problem of qualitatively recovering a supported cavity in a thin elastic plate governed by the flexural (biharmonic) wave equation, using far-field pattern measurements. We derive a reciprocity principle and a…
We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves, interior transmission eigenfunctions, and their applications to…
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…
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 are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
The goal of this paper is to develop numerical methods computing a few smallest elastic interior transmission eigenvalues, which are of practical importance in inverse elastic scattering theory. The problem is challenging since it is…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
This paper concerns the time-harmonic direct and inverse elastic scattering by an extended rigid elastic body surrounded by a finite number of point-like obstacles. We first justify the point-interaction model for the Lam\'{e} operator…
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…
This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface…