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Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…

Analysis of PDEs · Mathematics 2025-11-06 Thorsten Hohage , Meng Liu

We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-\'Emery Laplacian $-\Delta_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary…

Analysis of PDEs · Mathematics 2025-04-03 Jack Borthwick , Niky Kamran

We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…

Analysis of PDEs · Mathematics 2026-01-19 Emilia L. K. Blåsten , Tapio Helin , Antti Kujanpää , Lauri Oksanen , Jesse Railo

This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…

Numerical Analysis · Mathematics 2024-12-10 Yan Chang , Yukun Guo , Zhipeng Yang , Yue Zhao

We study two inverse problems on a globally hyperbolic Lorentzian manifold $(M,g)$. The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood $V\subset M$ of a time-like geodesic $\mu$. Under natural…

Differential Geometry · Mathematics 2017-09-22 Yaroslav Kurylev , Matti Lassas , Gunther Uhlmann

We study Maxwell's equations in time domain in an anisotropic medium. The goal of the paper is to solve an inverse boundary value problem for anisotropies characterized by scalar impedance $\alpha$. This means that the material is…

Analysis of PDEs · Mathematics 2007-05-23 Yaroslav Kurylev , Matti Lassas , Erkki Somersalo

This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

Analysis of PDEs · Mathematics 2026-01-19 Chengyu Wu , Jiaqing Yang

In this paper, we consider an inverse electromagnetic medium scattering problem of reconstructing unknown objects from time-dependent boundary measurements. A novel time-domain direct sampling method is developed for determining the…

Numerical Analysis · Mathematics 2024-10-11 Chen Geng , Minghui Song , Xianchao Wang , Yuliang Wang

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

Numerical Analysis · Mathematics 2025-10-24 Kai Yu , Zhiyuan Li , Yikan Liu

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

Analysis of PDEs · Mathematics 2018-12-03 Jianliang Li , Tapio Helin , Peijun Li

We study inverse boundary problems for semilinear Schr\"odinger equations on smooth compact Riemannian manifolds of dimensions $\ge 2$ with smooth boundary, at a large fixed frequency. We show that certain classes of cubic nonlinearities…

Analysis of PDEs · Mathematics 2024-02-21 Katya Krupchyk , Shiqi Ma , Suman Kumar Sahoo , Mikko Salo , Simon St-Amant

In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…

Analysis of PDEs · Mathematics 2018-12-24 Yu Zhao , Guanghui Hu , Baoqiang Yan

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…

Analysis of PDEs · Mathematics 2020-04-29 Jingzhi Li , Hongyu Liu , Shiqi Ma

For a compact Riemannian manifold $(M,g)$ with boundary $\partial M$, the Diri\-chl\-et-to-Neumann operator $\Lambda_g:C^\infty(\partial M)\longrightarrow C^\infty(\partial M)$ is defined by $\Lambda_gf=\left.\frac{\partial…

Differential Geometry · Mathematics 2025-01-30 Vladimir A. Sharafutdinov

This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…

Numerical Analysis · Mathematics 2021-01-14 Xiaoli Feng , Meixia Zhao , Peijun Li , Xu Wang

This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…

Numerical Analysis · Mathematics 2025-04-29 Chunlong Sun , Wenlong Zhang , Zhidong Zhang

The linear Boltzmann equation governs the absorption and scattering of a population of particles in a medium with an ambient field, represented by a Riemannian metric, where particles follow geodesics. In this paper, we study the possible…

Analysis of PDEs · Mathematics 2023-05-16 Zouhour Rezig

Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions…

Differential Geometry · Mathematics 2018-03-20 Matti Lassas , Teemu Saksala , Hanming Zhou

We study an inverse scattering problem for Maxwell's equations in terminating waveguides, where localized reflectors are to be imaged using a remote array of sensors. The array probes the waveguide with waves and measures the scattered…

Numerical Analysis · Mathematics 2015-10-27 Liliana Borcea , Dinh-Liem Nguyen

In this paper, we study the inverse boundary value problem for the wave equation with a view towards an explicit reconstruction procedure. We consider both the anisotropic problem where the unknown is a general Riemannian metric smoothly…

Analysis of PDEs · Mathematics 2017-10-10 Maarten de Hoop , Paul Kepley , Lauri Oksanen