eprintid: 10133487
rev_number: 22
eprint_status: archive
userid: 608
dir: disk0/10/13/34/87
datestamp: 2021-09-10 15:07:18
lastmod: 2021-09-22 22:27:39
status_changed: 2021-09-10 15:07:18
type: article
metadata_visibility: show
creators_name: Jin, B
creators_name: Zhou, Z
title: Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source *
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
divisions: F48
keywords: Inverse potential problem, subdiffusion, unknown medium, order
determination, numerical reconstruction
note: 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.
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.
date: 2021-10
date_type: published
publisher: IOP Publishing
official_url: https://doi.org/10.1088/1361-6420/ac1f6d
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1883666
doi: 10.1088/1361-6420/ac1f6d
lyricists_name: Jin, Bangti
lyricists_id: BJINX59
actors_name: Zahnhausen-Stuber, Petra
actors_id: PMZAH20
actors_role: owner
full_text_status: public
publication: Inverse Problems
volume: 37
number: 10
article_number: 105009
citation:        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 <https://doi.org/10.1088/1361-6420%2Fac1f6d>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10133487/10/Jin_2021_Inverse_Problems_37_105009.pdf