标题： 一维次扩散的逆系数问题，时间数据在不相交的集合上 显示英文标题

标题： Inverse Coefficient Problem for One-Dimensional Subdiffusion with Data on Disjoint Sets in Time

摘要： 在本工作中，我们研究了一维次扩散模型的逆系数问题，该问题涉及时间上的Caputo分数阶导数。 逆问题是从一对侧向柯西数据中确定两个系数和多个参数（顺序和区间长度）。 侧向柯西数据在时间上不相交的集合上给出，仅使用一次激励，测量是在激励支撑区域之外的时间序列上进行的。 我们证明了针对不同侧向柯西数据的两个唯一性结果。 分析基于解的表示、观测的解析性以及Sini [35] 的反Sturm-Liouville理论的改进版本。 我们的结果充分利用了分数阶扩散的记忆效应，以唯一恢复模型中的系数。 还进行了若干数值实验以补充分析。 显示英文摘要

摘要： In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the order, and length of the interval) from one pair of lateral Cauchy data. The lateral Cauchy data are given on disjoint sets in time with a single excitation and the measurement is made on a time sequence located outside the support of the excitation. We prove two uniqueness results for different lateral Cauchy data. The analysis is based on the solution representation, analyticity of the observation and a refined version of inverse Sturm-Liouville theory due to Sini [35]. Our results heavily exploit the memory effect of fractional diffusion for the unique recovery of the coefficients in the model. Several numerical experiments are also presented to complement the analysis.