A frequency-domain method to inverse moving source problem with unknown radiating moment
School of Mathematical Sciences, Sichuan Normal University（四川师范大学数学科学学院）；School of Mathematical Sciences and Institute of Mathematics and Interdisciplinary Sciences, Tianjin Normal University（天津师范大学数学科学学院与数学交叉科学研究所）；School of Mathematical Sciences and LPMC, Nankai University（南开大学数学科学学院与理论物理研究中心）
This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we establish a computational criterion that characterizes both the unknown pulse moments and the narrowest strip (perpendicular to the direction) enclosing the source support. Central to our inversion scheme is the construction of indicator functions, defined pointwise over the spatial and temporal sampling variables. The proposed inversion scheme permits the recovery of the $Θ$-convex support domain from far-field data at sparse observation directions. Uniqueness in determining the convex hull of the support and the excitation instants-using all observation directions-is also established as a direct consequence of the factorization method. The effectiveness and feasibility of the approach are examined through comprehensive numerical simulations in two and three dimensions.
A novel sampling method for reconstruction of a moving point acoustic source in $\mathbb{R}^3$
School of Mathematical Sciences, Sichuan Normal University（四川师范大学数学科学学院）；Institute of Mathematics and Interdisciplinary Sciences, Tianjin Normal University（天津师范大学数学与交叉科学研究院）
Rapid Identification of Moving Contaminant Sources Through Physics-Based Modelling
German Aerospace Center (DLR), Institute for the Protection of Terrestrial Infrastructures（德国航空航天中心（DLR）陆地基础设施保护研究所）；University of the Bundeswehr Munich, Institute for Mathematics and Computer-Based Simulation (IMCS)（慕尼黑联邦国防大学数学与计算机仿真研究所）
