带周期边界条件时间分数阶扩散方程逆时反问题的条件稳定性

Conditional stability of backward problem for a time fractional diffusion equation with periodic boundary condition

基于伴随思想,利用分离变量方法研究了一类带周期边界条件时间分数阶扩散方程,首先在弱解意义下推得了正问题解的正则性,然后基于对初值的光滑性假设推得了逆时反问题条件稳定性结论.

Based on the adjoint idea,a kind of time fractional diffusion equation with periodic boundary condition by method of separation of variables was considered.Firstly,the regularization result of the solution to the direct problem in the sense of weak solution was derived.Then based on the smoothing assumption for the initial data,the conditional stability for the backward problem was gived.