Jin, B;
Kian, Y;
Zhou, Z;
(2021)
Reconstruction of a Space-Time Dependent Source in Subdiffusion Models via a Perturbation Approach.
SIAM Journal on Mathematical Analysis
, 53
(4)
pp. 4445-4473.
10.1137/21M1397295.
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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 $\alpha\in(0,1)$ 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.
| Type: | Article |
|---|---|
| Title: | Reconstruction of a Space-Time Dependent Source in Subdiffusion Models via a Perturbation Approach |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/21M1397295 |
| Publisher version: | ttps://doi.org/10.1137/21M1397295 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Inverse source problem, subdiffusion, time-dependent coefficient, conditional stability, reconstruction |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10128332 |
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