Inverse Problems for Subdiffusion from Observation at an Unknown Terminal Time
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Publication:6168011
DOI10.1137/22M1529105zbMATH Open1525.35247arXiv2210.07589OpenAlexW4384498952MaRDI QIDQ6168011
Author name not available (Why is that?)
Publication date: 8 August 2023
Published in: (Search for Journal in Brave)
Abstract: Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years. However, all existing studies have assumed that the terminal time at which one takes the observation is exactly known. In this work, we present uniqueness and stability results for three canonical inverse problems, e.g., backward problem, inverse source and inverse potential problems, from the terminal observation at an unknown time. The subdiffusive nature of the problem indicates that one can simultaneously determine the terminal time and space-dependent parameter. The analysis is based on explicit solution representations, asymptotic behavior of the Mittag-Leffler function, and mild regularity conditions on the problem data. Further, we present several one- and two-dimensional numerical experiments to illustrate the feasibility of the approach.
Full work available at URL: https://arxiv.org/abs/2210.07589
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