论文标题
次扩散的一个反向潜在问题：稳定性和重建
An Inverse Potential Problem for Subdiffusion: Stability and Reconstruction
论文作者
论文摘要
在这项工作中，我们研究了在次扩散模型中恢复潜在系数的反问题，该模型涉及从终端数据中的djrbashian-caputo导数（0,1）$ in（0,1）$。我们证明，在初始数据的某些条件下，逆问题是局部lipschitz的小终端时间。该结果将标准抛物线病例的Choulli和Yamamoto（1997）扩展到了分数情况。该分析依赖于两参数Mittag-Leffler函数的精致性质，例如完全单调性和渐近性。此外，我们开发了一种有效且易于实现的算法，用于基于（预处理的）固定点迭代和安德森加速度来恢复该系数。用几个数值示例说明了算法的效率和准确性。
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 $α\in(0,1)$ 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.
