论文标题
在未知终端时间观察的次扩散的逆问题
Inverse Problems for Subdiffusion from Observation at an Unknown Terminal Time
论文作者
论文摘要
近年来，已经对终端观察的次扩散模型中的初始条件，依赖空间依赖的源或潜在系数的逆问题进行了广泛的研究。但是，所有现有的研究都假设一个人进行观察的终端时间是完全已知的。在这项工作中，我们从未知时间的终端观察中提出了三个规范反问题的唯一性和稳定性结果，例如向后问题，反向源和反向潜在问题。问题的宽大性质表明，可以同时确定终端时间和空间依赖性参数。该分析基于明确的解决方案表示，Mittag-Leffler函数的渐近行为以及问题数据的轻度规律条件。此外，我们提出了几个一维数值实验，以说明该方法的可行性。
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.
