Jin, B;
Zhou, Z;
(2021)
Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *.
Inverse Problems
, 37
(10)
, Article 105009. 10.1088/1361-6420/ac1f6d.
Preview |
Text
Jin_2021_Inverse_Problems_37_105009.pdf - Published Version Download (1MB) | Preview |
Abstract
This paper is concerned with an inverse problem of recovering a potential term and fractional order in a one-dimensional subdiffusion problem, which involves a Djrbashian–Caputo fractional derivative of order α ∈ (0, 1) in time, from the lateral Cauchy data. In the model, we do not assume a full knowledge of the initial data and the source term, since they might be unavailable in some practical applications. We prove the unique recovery of the spatially-dependent potential coefficient and the order α of the derivation simultaneously from the measured trace data at one end point, when the model is equipped with a boundary excitation with a compact support away from t = 0. One of the initial data and the source can also be uniquely determined, provided that the other is known. The analysis employs a representation of the solution and the time analyticity of the associated function. Further, we discuss a two-stage procedure, directly inspired by the analysis, for the numerical identification of the order and potential coefficient, and illustrate the feasibility of the recovery with several numerical experiments.
| Type: | Article |
|---|---|
| Title: | Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source * |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1361-6420/ac1f6d |
| Publisher version: | https://doi.org/10.1088/1361-6420/ac1f6d |
| 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. |
| Keywords: | Inverse potential problem, subdiffusion, unknown medium, order determination, numerical 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/10133487 |
Loading...
Loading...Loading...Loading...Archive Staff Only
 |
View Item |
