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Title: | Recovering the potential and order in one-dimensional time-fractional diffusion with unknown initial condition and source | Authors: | Jin, B Zhou, Z |
Issue Date: | 2021 | Source: | Inverse problems, 2021, v. 37, no. 10, 105009 | 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. | Keywords: | Inverse potential problem Numerical reconstruction Order determination Subdiffusion Unknown medium |
Publisher: | Institute of Physics Publishing Ltd. | Journal: | Inverse problems | ISSN: | 0266-5611 | EISSN: | 1361-6420 | DOI: | 10.1088/1361-6420/ac1f6d | Rights: | © 2021 The Author(s). Published by IOP Publishing Ltd Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence (https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. The following publication 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), 105009 is available at https://doi.org/10.1088/1361-6420/ac1f6d. |
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