节点文献
IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION
【摘要】 In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution(if it exists) does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.
【Abstract】 In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution(if it exists) does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.
【Key words】 spatial-dependent heat source； space-fractional diffusion equation； generalized Tikhonov regularization； A posteriori parameter choice； error estimate；
- 【文献出处】 Acta Mathematica Scientia ,数学物理学报(英文版) , 编辑部邮箱 ,2014年04期
- 【分类号】O175
- 【被引频次】4
- 【下载频次】22