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This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…

Analysis of PDEs · Mathematics 2024-08-01 Adel Blouza , Léo Glangetas , Yavar Kian , Van-Sang Ngo

We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…

Analysis of PDEs · Mathematics 2023-03-10 Yi-Hsuan Lin , Hongyu Liu , Xu Liu

In this work the authors consider the recovery of the point source in the heat equation. The used data is the sparse boundary measurements. The uniqueness theorem of the inverse problem is given. After that, the numerical reconstruction is…

Numerical Analysis · Mathematics 2025-02-06 Qiling Gu , Wenlong Zhang , Zhidong Zhang

Inverse Problem techniques offer powerful tools which deal naturally with marginal data and asymmetric or strongly smoothing kernels, in cases where parameter-fitting methods may be used only with some caution. Although they are typically…

Astrophysics · Physics 2007-05-23 Norman Gray , Iain J. Coleman

We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for…

Analysis of PDEs · Mathematics 2023-06-02 Mansur I. Ismailov , Tohru Ozawa , Durvudkhan Suragan

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…

Analysis of PDEs · Mathematics 2020-04-08 Elham Sohrabi

We study the problem of recovery the source $a(t,x)F(x)$ in the wave equation in anisotropic medium with $a$ known so that $a(0,x)\not=0$ with a single measurement. We use Carleman estimates combined with geometric arguments and give sharp…

Analysis of PDEs · Mathematics 2011-03-08 Plamen Stefanov , Gunther Uhlmann

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…

Optimization and Control · Mathematics 2021-03-30 Konstantin Pieper , Bao Quoc Tang , Philip Trautmann , Daniel Walter

This paper is concerned with inverse source problems for the acoustic wave equation in the full space R^3, where the source term is compactly supported in both time and spatial variables. The main goal is to investigate increasing stability…

Analysis of PDEs · Mathematics 2024-03-14 Chun Liu , Suliang Si , Guanghui Hu , Bo Zhang

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…

Analysis of PDEs · Mathematics 2020-09-23 Anna Kirpichnikova , Jussi Korpela , Matti Lassas , Lauri Oksanen

Study of a simple single-trace transmission example shows how an extended source formulation of full-waveform inversion can produce an optimization problem without spurious local minima ("cycle skipping"), hence efficiently solvable via…

Optimization and Control · Mathematics 2022-09-28 William W. Symes , Huiyi Chen , Susan E. Minkoff

Given near or far field wave measurements generated by some unknown time- and space-dependent acoustic source, we seek to rapidly determine a domain in space-time, as small as possible, that contains the support of a source radiating these…

Analysis of PDEs · Mathematics 2016-07-07 Armin Lechleiter

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…

Analysis of PDEs · Mathematics 2026-03-06 Rodrigo Lecaros , Ariel A. Pérez , Manuel F. Prado

In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…

Analysis of PDEs · Mathematics 2022-07-15 Jaan Janno , Yavar Kian

A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.

Analysis of PDEs · Mathematics 2011-11-10 Katsiaryna Krupchyk , Matti Lassas

This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…

Numerical Analysis · Mathematics 2026-03-11 Fenglin Sun , Hongxia Guo

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Analysis of PDEs · Mathematics 2026-02-24 Daniela Di Donato , Luca Rondi

In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time…

Analysis of PDEs · Mathematics 2024-12-12 Kuang Huang , Bangti Jin , Yavar Kian , Georges Sadaka , Zhi Zhou

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is the translation invariance. Thus it is impossible to reconstruct the location of the…

Analysis of PDEs · Mathematics 2018-08-08 Xia Ji , Xiaodong Liu , Bo Zhang

This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…

Analysis of PDEs · Mathematics 2026-03-13 Mohamed BenSalah , Yikan Liu