Jin, B;
Zhou, Z;
(2021)
An Inverse Potential Problem for Subdiffusion: Stability and Reconstruction.
Inverse Problems
, 37
(1)
, Article 015006. 10.1088/1361-6420/abb61e.
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Abstract
In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbahsian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse problem is locally Lipschitz for small terminal time, under certain conditions on the initial data. This result extends the result in \cite{ChoulliYamamoto:1997} for the standard parabolic case. The analysis relies on refined properties of two-parameter Mittag-Leffler functions, e.g., complete monotonicity and asymptotics. Further, we develop an efficient algorithm for numerically recovering the coefficient based on (preconditioned) fixed point iteration and Anderson acceleration. The efficiency and accuracy of the algorithm is illustrated with several numerical examples.
| Type: | Article |
|---|---|
| Title: | An Inverse Potential Problem for Subdiffusion: Stability and Reconstruction |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1361-6420/abb61e |
| Publisher version: | https://doi.org/10.1088/1361-6420/abb61e |
| Language: | English |
| Additional information: | Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. https://creativecommons.org/licenses/by/4.0/ |
| 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/10109733 |
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