TY - JOUR
T1 - Reconstruction of a space-time dependent source in subdiffusion models via a perturbation approach
AU - Jin, Bangti
AU - Kian, Yavar
AU - Zhou, Zhi
N1 - 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 ([email protected]). \ddagger Aix-Marseille University, Universit\e' de Toulon, CNRS, CPT, Marseille, France ([email protected]). \S Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong ([email protected]).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.
PY - 2021/7
Y1 - 2021/7
N2 - 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.
AB - 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.
KW - Conditional stability
KW - Inverse source problem
KW - Reconstruction
KW - Subdiffusion
KW - Time-dependent coefficient
UR - http://www.scopus.com/inward/record.url?scp=85113284646&partnerID=8YFLogxK
U2 - 10.1137/21M1397295
DO - 10.1137/21M1397295
M3 - Journal article
SN - 0036-1410
VL - 53
SP - 4445
EP - 4473
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 4
ER -