论文标题
时间分数进化方程的向后问题
The backward problem for time fractional evolution equations
论文作者
论文摘要
在本文中，我们考虑了分数的时间演变方程的向后问题$ \ partial_t^αu（t）= a u（t）$ a caputo derivativative $ 0 <α\ le 1 $，其中$ a $是一个自动化和界限，并且在Hilbert Space $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h。首先，我们通过分析Mittag-Leffler函数的属性，将对数凸技术扩展到分数框架。然后，在最终数据的较弱规范下，我们证明了Hölder类型的有条件稳定性估计值。最后，我们提供了几个应用程序，以显示我们的抽象结果的适用性。
In this paper, we consider the backward problem for fractional in time evolution equations $\partial_t^αu(t)= A u(t)$ with the Caputo derivative of order $0<α\le 1$, where $A$ is a self-adjoint and bounded above operator on a Hilbert space $H$. First, we extend the logarithmic convexity technique to the fractional framework by analyzing the properties of the Mittag-Leffler functions. Then we prove conditional stability estimates of Hölder type for initial conditions under a weaker norm of the final data. Finally, we give several applications to show the applicability of our abstract results.
