Related papers: An inverse moving point source problem in electrom…
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…
The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inverse source problem, which involves determining the random…
The paper derived differential equations which solve the problem of restoration the motion parameters for a rigid reference frame from the known proper acceleration and angular velocity of its origin as functions of proper time. These…
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running…
Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches…
We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusive regime (the Knudsen number $\mathsf{Kn}\ll 1$), the…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen,…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…
Through coupled physics, we study an early-warning inverse source problem for the elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and…
We analyze the inverse problem, originally formulated by Dix in geophysics, of reconstructing the wave speed inside a domain from boundary measurements associated with the single scattering of seismic waves. We consider a domain $\tilde M$…
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…
We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…
We propose in this paper a new numerical method to solve an inverse source problem for general hyperbolic equations. This is the problem of reconstructing sources from the lateral Cauchy data of the wave field on the boundary of a domain.…
This paper is devoted to the inverse problem of recovering simultaneously a potential and a point source in a Shr\"odinger equation from the associated nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved and…
We consider a smooth Riemannian metric tensor $g$ on $\R^n$ and study the stochastic wave equation for the Laplace-Beltrami operator $\p_t^2 u - \Delta_g u = F$. Here, $F=F(t,x,\omega)$ is a random source that has white noise distribution…