Jin, Bangti; Shin, Kwancheol; Zhou, Zhi; (2024) Numerical recovery of a time-dependent potential in subdiffusion. Inverse Problems , 40 (2) , Article 025008. 10.1088/1361-6420/ad14a0.

Text Jin_2311.02420.pdf - Accepted Version Access restricted to UCL open access staff until 29 December 2024. Download (1MB)

Abstract

In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian–Caputo fractional derivative in time. Theoretically, we prove a novel conditional Lipschitz stability result, and numerically, we develop an easy-to-implement fixed point iteration for recovering the unknown coefficient. In addition, we establish rigorous error bounds on the discrete approximation. These results are obtained by crucially using smoothing properties of the solution operators and suitable choice of a weighted L p (0, T) norm. The efficiency and accuracy of the scheme are showcased on several numerical experiments in one- and two-dimensions.

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