@article{4b8e24315dd44cb8b4e730e5c35665de,
title = "Reconstruction of a space-time dependent source in subdiffusion models via a perturbation approach",
abstract = "In this article we study two inverse problems of recovering a space-time-dependent source component from the lateral boundary observation in a subdiffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of order α ∊ (0, 1) in time, and a second-order elliptic operator with time-dependent coefficients. We establish a well-posedness and a conditional stability result for the inverse problems using a novel perturbation argument and refined regularity estimates of the associated direct problem. Further, we present a numerical algorithm for efficiently and accurately reconstructing the source component, and we provide several two-dimensional numerical results showing the feasibility of the recovery.",
keywords = "Conditional stability, Inverse source problem, Reconstruction, Subdiffusion, Time-dependent coefficient",
author = "Bangti Jin and Yavar Kian and Zhi Zhou",
note = "Funding Information: \ast Received by the editors February 5, 2021; accepted for publication (in revised form) May 10, 2021; published electronically August 10, 2021. https://doi.org/10.1137/21M1397295 Funding: The work of the first author was partially supported by UK EPSRC grant EP/T000864/1. The work of the second author was supported by the French National Research Agency ANR (project MultiOnde) through grant ANR-17-CE40-0029. The work of the third author was supported by Hong Kong RGC grant 15304420. \dagger Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK (b.jin@ucl.ac.uk). \ddagger Aix-Marseille University, Universit\e' de Toulon, CNRS, CPT, Marseille, France (yavar.kian@univ-amu.fr). \S Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (zhi.zhou@polyu.edu.hk). Publisher Copyright: {\textcopyright} 2021 Society for Industrial and Applied Mathematics.",
year = "2021",
month = jul,
doi = "10.1137/21M1397295",
language = "English",
volume = "53",
pages = "4445--4473",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}