A mollification regularization method for unknown source in time-fractional diffusion equation

被引：29
|
作者：
Yang, Fan [1 ,2 ]
Fu, Chu-Li [2 ]
Li, Xiao-Xiao [1 ]
机构：
[1] Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Gansu, Peoples R China
[2] Lanzhou Univ Technol, Sch Math & Stat, Lanzhou 730050, Gansu, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2014年 / 91卷 / 07期
基金：
中国国家自然科学基金;
关键词：
time-dependent heat source; time-fractional diffusion equation; modified regularization; a posteriori parameter choice; error estimate; DEPENDENT HEAT-SOURCE; INVERSE SOURCE PROBLEM; SOURCE-TERM; CONDITIONAL STABILITY; ANOMALOUS DIFFUSION;
D O I：
10.1080/00207160.2013.851787
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1516 / 1534
页数：19
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