Data regularization for a backward time-fractional diffusion problem

作者：Wang, Liyan; Liu, Jijun^*

来源：Computers & Mathematics with Applications, 2012, 64(11): 3613-3626.

DOI：10.1016/j.camwa.2012.10.001

• Backward problem
• Diffusion process
• Fractional derivative
• Regularization
• Data fitting
• Numerics

We investigate a backward problem for a time-fractional diffusion process in inhomogeneous media, which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data. This problem is well-known to be ill-posed due to the rapid decay of the forward process. By using the eigenfunction expansion, we construct a new regularizing scheme with an explicit solution for the noisy input data with the number of truncation terms as a regularizing parameter. The convergence rate depending on the choice of strategy of the regularizing parameter is given based on the asymptotic behavior of the Mittag-Leffler function. Numerical implementations are presented to show the validity of the proposed scheme for several models.

• 出版日期2012-12
• 单位东南大学