论文标题
具有可变系数的时空分数抛物线运算符的Calderón问题
The Calderón problem for space-time fractional parabolic operators with variable coefficients
论文作者
论文摘要
我们研究了$（\ partial_t- \ perperatorName {div}（a（x）\ nabla_x）^s + q（x，x，t）$ for（0,1）$的$ s \ in（0,1）$的$ q $ quontim formim for e ellipt for frimim for fractim for frimim for frimim for frimim for frimim forime，通过全球弱的延续性属性获得的证明，涉及与工作后期的相关变量系数延长运算符的新卡尔曼估计。
We study an inverse problem for variable coefficient fractional parabolic operators of the form $(\partial_t -\operatorname{div}(A(x) \nabla_x)^s + q(x,t)$ for $s\in(0,1)$ and show the unique recovery of $q$ from exterior measured data. Similar to the fractional elliptic case, we use Runge type approximation argument which is obtained via a global weak unique continuation property. The proof of such a unique continuation result involves a new Carleman estimate for the associated variable coefficient extension operator. In the latter part of the work, we prove analogous unique determination results for fractional parabolic operators with drift.
