论文标题
及时及时的较向后问题的适应性，用于一般的时间分数扩散方程
Well-posedness for the backward problems in time for general time-fractional diffusion equation
论文作者
论文摘要
在本文中，我们考虑了带有CAPUTO时间衍生的部分微分方程：$ \ partial_t^αu + au = f $其中$ 0 <α<1 $ and $ u $满足零dirichlet边界条件。对于第二订单的非对称椭圆操作员$ -A $ -A $，我们证明了时间及时的向后问题的适应性，我们的结果概括了现有结果，假设$ a $是对称的。关键是椭圆运算符$ a $的扰动参数和通用特征函数的完整性。
In this article, we consider a partial differential equation with Caputo time-derivative: $\partial_t^αu + Au = F$ where $0< α< 1$ and $u$ satisfies the zero Dirichlet boundary condition. For a non-symmetric elliptic operator $-A$ of the second order and given $F$, we prove the well-posedness for the backward problem in time and our result generalizes the existing results assuming that $A$ is symmetric. The key is the perturbation argument and the completeness of the generalized eigenfunctions of the elliptic operator $A$.
