时间分数阶扩散方程逆向问题的迭代分数次Tikhonov方法
Iterated Fractional Tikhonov Method for a Backward Problem for the Time-Fractional Diffusion Equation
摘要: 研究了一个在一般有界域中的具有可变系数的时间分数阶扩散方程的逆向问题。提出了一种迭代的分数次Tikhonov正则化方法去解决这个逆向问题。此外，通过先验正则化参数选取规则和后验正则化参数选取规则，证明了正则化解的收敛率。迭代的分数次Tikhonov正则化方法超越了经典Tikonov正则化方法的饱和结果，在先验参数选取规则下，迭代的分数次Tikhonov正则化方法优于经典迭代Tikonov正则化方法。
Abstract: The backward problem of a time-fractional diffusion equation with variable coefficients in a general bounded domain is studied. An iterative fractional Tikhonov regularization method was proposed to solve the backward problem. In addition, the convergence rates for the regularized solution can be proved by using an a priori regularization parameter choice rule and an a posteriori regulariza-tion parameter choice rule. The iterative fractional Tikhonov regularization method surpasses the saturation result of classical Tikhonov regularization method, and iterative fractional Tikhonov regularization method is superior to classical iterative Tikhonov regularization method under the a-priori parameter choice rule.
文章引用：杜文慧. 时间分数阶扩散方程逆向问题的迭代分数次Tikhonov方法[J]. 应用数学进展, 2023, 12(4): 1792-1803. https://doi.org/10.12677/AAM.2023.124186

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