论文标题
在未知介质中恢复分布式阶分数衍生物
Recovery of a Distributed Order Fractional Derivative in an Unknown Medium
论文作者
论文摘要
在这项工作中，我们研究了一个逆问题，即恢复分布式订购时间分数分数扩散的信息，从域边界上的一个点处的观察值。在没有对介质的明确知识的情况下，我们证明单点观察可以唯一地确定重量的支撑界。该证明基于数据，分析延续和Titchmarch卷积定理的渐近学。当已知介质时，我们给出了现有结果的替代证明，即，单点边界观察结果独特地决定了重量。还提出了一些数值实验以补充分析。
In this work, we study an inverse problem of recovering information about the weight in distributed-order time-fractional diffusion from the observation at one single point on the domain boundary. In the absence of an explicit knowledge of the medium, we prove that the one-point observation can uniquely determine the support bound of the weight. The proof is based on asymptotics of the data, analytic continuation and Titchmarch convolution theorem. When the medium is known, we give an alternative proof of an existing result, i.e., the one-point boundary observation uniquely determines the weight. Several numerical experiments are also presented to complement the analysis.
