The Calderón Problem for a Space-Time Fractional Parabolic Equation
The Calderón Problem for a Space-Time Fractional Parabolic Equation
复制标题
时空分数阶抛物型方程的卡尔德隆问题
DOI：
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发表时间：
2019
影响因子：
2
通讯作者：
Angkana Rüland
中科院分区：
文献类型：
--
作者：
Ru;Yi;Angkana Rüland
本文研究了时空分数次抛物算子$(Partial_t-Delta)、S+q$在任意空间维中具有$0<；S；1$的反问题。我们从无穷多个外部Dirichlet-to-Neumann型测量唯一地确定未知有界势$q$。这依赖于Runge逼近和所考虑方程的对偶整体弱唯一延拓性质。在讨论算子的弱唯一延拓时，我们论证的一个主要特征依赖于相关的分数抛物型Caffarelli-Silvestre延拓的Carleman估计。此外，我们还讨论了基于方程的逼近和唯一连续性质的构造性的单次测量结果。
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 Carleman estimate for the associated fractional parabolic Caffarelli-Silvestre extension. Furthermore, we also discuss constructive single measurement results based on the approximation and unique continuation properties of the equation.
DOI：
10.1080/03605300902740395
发表时间：
2009-01-01
影响因子：
1.9
作者：
Koch, Herbert;Tataru, Daniel
通讯作者：
Tataru, Daniel