一类空间分数阶扩散逆时问题的正则化方法与后验收敛性估计  

Regularization Method and A-posteriori Convergence Estimate for a Space-fractional Diffusion Problem Backward in Time

作　　者：张宏武 吕拥 ZHANG Hongwu;LV Yong(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《应用数学》2022年第1期110-119,共10页Mathematica Applicata

基　　金：Supported by the NSF of China (11761004);Construction Project of First-Class Disciplines in Ningxia Higher Education (NXYLXK2017B09)。

摘　　要：本文研究一类空间分数阶扩散逆时问题.基于条件稳定性结果,发展一种广义吉洪诺夫正则化方法克服其不适定性,并且通过正则化参数的后验选取规则获得正则化方法对数和双对数型收敛性估计.一些数值模拟结果验证了该方法的收敛性与稳定性.The article researches a space-fractional diffusion problem backward in time.Based on the result of conditional stability, we develop a generalized Tikhonov regularization method to overcome the ill-posedness of this problem, and then obtain the convergence estimates of logarithmic and double logarithmic types for the regularized method by the a-posteriori choice rules of regularization parameter. Some results of numerical simulations verify the convergence and stability for this method.

关 键 词：不适定问题 空间分数阶扩散问题 正则化方法 后验收敛性估计 数值模拟 

分 类 号：O175.24[理学—数学] O175.26[理学—基础数学]