In this work, we study the inverse problem of recovering a potential coefficient in the subdiffusion model, which involves a Djrbashian-Caputo derivative of order $\alpha\in(0,1)$ in time, from the terminal data. We prove that the inverse problem is locally Lipschitz for small terminal time, under certain conditions on the initial data. This result extends the result in Choulli and Yamamoto (1997) for the standard parabolic case to the fractional case. The analysis relies on refined properties of two-parameter Mittag-Leffler functions, e.g., complete monotonicity and asymptotics. Further, we develop an efficient and easy-to-implement algorithm for numerically recovering the coefficient based on (preconditioned) fixed point iteration and Anderson acceleration. The efficiency and accuracy of the algorithm is illustrated with several numerical examples.

中文翻译：

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亚扩散的一个逆位势问题：稳定性和重构

在这项工作中，我们研究了从终端数据中恢复子扩散模型中潜在系数的逆问题，该模型涉及时间 $\alpha\in(0,1)$ 阶的 Djrbashian-Caputo 导数。我们证明了在初始数据的某些条件下，对于小的终端时间，逆问题是局部的 Lipschitz。该结果将 Choulli 和 Yamamoto (1997) 中标准抛物线情况的结果扩展到分数情况。该分析依赖于二参数 Mittag-Leffler 函数的精细属性，例如完全单调性和渐近性。此外，我们开发了一种高效且易于实现的算法，用于基于（预处理的）定点迭代和安德森加速度对系数进行数值恢复。