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This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…

Numerical Analysis · Mathematics 2025-11-04 Hao Gu , Tianjiao Wang , Xiang Xu , Yue Zhao

The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…

Numerical Analysis · Mathematics 2016-09-14 Balgaisha Mukanova , Vladimir G. Romanov

We deal with the inverse problem of reconstructing acoustic material properties or/and external sources for the time-domain acoustic wave model. The traditional measurements consist of repeated active (or passive) interrogations, as the…

Analysis of PDEs · Mathematics 2025-07-15 Soumen Senapati , Mourad Sini

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

We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…

Analysis of PDEs · Mathematics 2007-08-17 Matias Dahl , Anna Kirpichnikova , Matti Lassas

Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…

Analysis of PDEs · Mathematics 2019-06-06 Phuong Mai Nguyen , Loc Hoang Nguyen

Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the Lipschitz boundary of a bounded obstacle…

Analysis of PDEs · Mathematics 2020-06-15 Andrea Mantile , Andrea Posilicano

We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography,…

Analysis of PDEs · Mathematics 2019-06-18 Christina Knox , Amir Moradifam

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…

Numerical Analysis · Mathematics 2024-01-02 Hongxia Guo , Guanghui Hu

We consider the inverse source problem in the parabolic equation, where the unknown source possesses the semi-discrete formulation. Theoretically, we prove that the flux data from any nonempty open subset of the boundary can uniquely…

Numerical Analysis · Mathematics 2022-11-23 Guang Lin , Zecheng Zhang , Zhidong Zhang

In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…

Analysis of PDEs · Mathematics 2022-11-09 Hanin Al Jebawy , Abdellatif El Badia , Faouzi Triki

We propose a method to reconstruct the electrical current density from acoustically-modulated boundary measurements of time-harmonic electromagnetic fields. We show that the current can be uniquely reconstructed with Lipschitz stability. We…

Analysis of PDEs · Mathematics 2022-02-25 Wei Li , John C. Schotland , Yang Yang , Yimin Zhong

We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…

Analysis of PDEs · Mathematics 2015-05-18 Matti Lassas , Lauri Oksanen

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

Analysis of PDEs · Mathematics 2021-01-22 Guanghui Hu , Yavar Kian , Yue Zhao

Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a…

Differential Geometry · Mathematics 2023-08-09 Maarten V. de Hoop , Joonas Ilmavirta , Matti Lassas , Teemu Saksala

We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…

Analysis of PDEs · Mathematics 2023-05-10 Ali Feizmohammadi , Yavar Kian

We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.

Analysis of PDEs · Mathematics 2019-06-24 Manmohan Vashisth

A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…

Analysis of PDEs · Mathematics 2020-10-13 Loc H. Nguyen , Qitong Li , Michael V. Klibanov

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

Numerical Analysis · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…

Analysis of PDEs · Mathematics 2025-11-20 K. Van Bockstal , K. Khompysh