Related papers: Weakly singular corners always scatter
This work is concerned with an inverse electromagnetic scattering problem in two dimensions. We prove that in the TE polarization case, the knowledge of the electric far-field pattern incited by a single incoming wave is sufficient to…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…
We study time harmonic scattering for the Helmholtz equation in Rn. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission…
We investigate fixed energy scattering from conical potentials having an irregular cross-section. The incident wave can be any arbitrary non-trivial Herglotz wave. We show that a large number of such local conical scatterers scatter all…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
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…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far- or near-field measurement. We show that nonradiating sources having a convex or non-convex corner or edge on their…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…
This study describes both experimentally and theoretically an important hitherto undiscovered feature of the scattering of micron_sized spherical objects when illuminated with highly focused circularly polarized light. This is a regime of…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both `conductivity' in the divergence form and `potential' in the lower order term. The support of the inhomogeneity is assumed to contain a convex…
Starting from fundamental multiple scattering theory it is shown that negative refraction indices are feasible for matter waves passing a well-defined ensemble of scatterers. A simple approach to this topic is presented and explicit…
This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…
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…
This paper investigates the inverse scattering problem for the magnetic Schr\"odinger equation. We first establish the well-posedness of the direct problem through a variational approach under physically meaningful assumptions on the…
This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…
We study the scattering behavior of an anisotropic inhomogeneous Lipschitz medium at a fixed wave number, continuing our previous work [SIAM J. Math. Anal., 56(4):4834-4853, 2024] and using free boundary techniques from [arXiv:2506.22328].…