ABSTRACT

We proved the unique determination of the variable order in a two-scale mobile–immobile variable-order time-fractional partial differential equation with a variable diffusivity tensor imposed on a general multi-dimensional domain, with the observations of the unknown solutions on any arbitrarily small spatial domain over a sufficiently small time interval. The proved theorem provides a guidance where the measurements should be performed and ensures that with these observations the uniqueness of the identification is theoretically guaranteed.

中文翻译：

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在一般多维域上唯一识别时间分数偏微分方程的变阶

摘要

我们证明了两尺度移动-不动变阶时间分数偏微分方程中变阶的唯一确定，该偏微分方程具有施加在一般多维域上的可变扩散率张量，以及对任意任意解的未知解的观察在足够小的时间间隔内的小空间域。经证明的定理提供了应该在何处执行测量的指导，并确保通过这些观察，识别的唯一性在理论上得到保证。