时间分数阶扩散方程同时反演源项和初值的迭代分数次

Iterated fractional Tikhonov method for simultaneous inversion of the source term and initial data in time-fractional diffusion equations

研究了同时反演时间分数阶扩散方程的依赖空间的源项和初始值的反问题。这个反问题在傅里叶方法的基础上被重新表述为第一类算子方程。提出了一种迭代分数次Tikhonov正则化方法来解决该反问题。此外,还给出了先验正则化参数选择规则,并证明了相应的收敛估计。

The inverse problem of identifying the space-dependent source term and the initial value simultaneously for a time-fractional diffusion equation is investigated.This inverse problem is reformulated on the basis of Fourier method as operator equations of the first kind.An iterative fractional Tikhonov regularization method is proposed to solve this inverse problem.In addition,a prior regularization parameter choice rule is given and the corresponding convergence estimation is proved.