SIAM Journal on Mathematical Analysis, Volume 52, Issue 3, Page 2655-2688, January 2020.
In this article we study an inverse problem for the space-time fractional parabolic operator $(\partial_t-\Delta)^s+Q$ with $0<s<1$ in any space dimension. We uniquely determine the unknown bounded potential $Q$ from infinitely many exterior Dirichlet-to-Neumann type measurements. This relies on Runge approximation and the dual global weak unique continuation properties of the equation under consideration. In discussing weak unique continuation of our operator, a main feature of our argument relies on a new Carleman estimate for the associated degenerate parabolic Caffarelli--Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.

中文翻译：

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时空分数阶抛物方程的Calderón问题

SIAM数学分析杂志，第52卷，第3期，第2655-2688页，2020年1月。
在本文中，我们研究时空分数抛物算子$（\ partial_t- \ Delta）^ s + Q $的反问题，其中任意空间维中的$ 0 <s <1 $。我们通过无数次外部Dirichlet-to-Neumann类型测量来唯一确定未知的有界势$ Q $。这取决于Runge逼近和所考虑方程的对偶全局弱唯一连续性。在讨论算子的弱唯一连续性时，我们的论证的主要特征依赖于相关的退化抛物线Caffarelli-Silvestre扩展的新的Carleman估计。此外，我们还讨论了基于方程的逼近和唯一连续性的建设性单一测量结果。