A mollification regularization method for unknown source in time-fractional diffusion equation
A mollification regularization method for unknown source in time-fractional diffusion equation
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DOI：
10.1080/00207160.2013.851787
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发表时间：
2014-07
影响因子：
1.8
通讯作者：
Fan Yang;C. Fu;Xiao-Xiao Li-Xiao
中科院分区：
文献类型：
--
作者：
Fan Yang;C. Fu;Xiao-Xiao Li-Xiao
本文考虑一类分数阶扩散方程的逆源问题。这个问题是不适定的，即解决方案(如果存在)不连续依赖于数据。我们给出了软化正则化方法来解决这个问题。得到了精确解与其正则化近似解之间的先验误差估计。此外，还提出了一种新的后验参数选择准则，并得到了较好的误差估计。数值算例表明了该方法的正确性和有效性。
In the present paper, we consider an inverse source problem for a fractional diffusion equation. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We give the mollification regularization method to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, a new a posteriori parameter choice rule is also proposed and a good error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.