This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary measurement corresponding to a fairly general boundary excitation uniquely determines the order of the fractional derivative and the polygonal support of the diffusion coefficient, without knowing either the initial condition or the source. The uniqueness analysis further inspires the development of a robust numerical algorithm for recovering the fractional order and diffusion coefficient. The proposed algorithm combines small-time asymptotic expansion, analytic continuation of the solution and the level set method. We present extensive numerical experiments to illustrate the feasibility of the simultaneous recovery. In addition, we discuss the uniqueness of recovering general diffusion and potential coefficients from one single partial boundary measurement, when the boundary excitation is more specialized.

翻译：本文旨在研究在不完全已知介质中，通过单次部分边界侧向测量同时数值恢复次扩散模型中的多个参数。我们证明，在相当一般的边界激励下，对应的边界测量能唯一确定分数阶导数的阶数与扩散系数的多边形支撑，而无需已知初始条件或源项。唯一性分析进一步启发了用于恢复分数阶数目和扩散系数的稳健数值算法的开发。所提出的算法结合了短时间渐近展开、解的解析延拓及水平集方法。我们通过大量数值实验验证了同时恢复的可行性。此外，讨论了在边界激励更特殊的情况下，通过单次部分边界测量恢复一般扩散系数与势系数的唯一性。