Related papers: An inverse problem without the phase information
This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…
The forward problem here is the Cauchy problem for a 1D hyperbolic PDE with a variable coefficient in the principal part of the operator. That coefficient is the spatially distributed dielectric constant. The inverse problem consists of the…
This work analyzes the forward and inverse scattering series for scalar waves based on the Helmholtz equation and the diffuse waves from the time-independent diffusion equation, which are important PDEs in various applications. Different…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.
We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…
We investigate temporal scattering in lossless Drude media and reveal an overlooked role of the zero-frequency flat band associated with static polarization charge. This flat band forms an exceptional line spanning all wavenumbers and can…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…
We formulate a problem that can be viewed as a natural variation of the so-called Pompeiu or Schiffer problem in the context of scattering of plane waves for the Linear Helmholtz equation. For the two dimensional version of this variation,…
This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a newly…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
In this short note, we present a probabilistic perspective on the Schiffer's problem in the inverse scattering theory, which asks whether one can uniquely determine the shape of an unknown obstacle by a single far-field measurement. It is a…
The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of…
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…
We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the…
This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can…