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Backward problem for time-space fractional diffusion equations in Hilbert scales
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-04-29 , DOI: 10.1016/j.camwa.2021.04.018
Dang Duc Trong , Dinh Nguyen Duy Hai

This work is concerned with a mathematical study of backward problem for time-space fractional diffusion equations associated with the observed data measured in Hilbert scales. Transforming the original problem into an operator equation, we investigate the existence, the uniqueness and the instability for the problem. In order to overcome the ill-posedness of the problem, we apply a modified version of quasi-boundary value method to construct stable approximation problem. Using a Hölder-type smoothness assumption of the exact solution it is shown that estimates achieve optimal rates of convergence in Hilbert scales both for an a-priori and for an a-posteriori parameter choice strategies.



中文翻译:

希尔伯特尺度上的时空分数扩散方程的后向问题

这项工作与时空分数扩散方程的后向问题的数学研究有关,后者与以希尔伯特尺度测量的观测数据相关。将原始问题转化为一个算子方程,我们研究该问题的存在性,唯一性和不稳定性。为了克服该问题的不适定性,我们应用了拟边界值方法的改进版本来构造稳定的逼近问题。使用精确解的Hölder型平滑度假设,可以证明,对于先验参数和后验参数选择策略,估计都可以达到希尔伯特量表的最优收敛速度。

更新日期:2021-04-30
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