IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

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...

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Bibliographic Details
Published in:Acta mathematica scientia 2014-07, Vol.34 (4), p.1012-1024
Main Author: 杨帆 傅初黎 李晓晓
Format: Article
Language:English
Subjects:
35R30
47A52
65M30
65M32
A posteriori parameter choice
Approximation
Diffusion
error estimate
Errors
Estimates
Exact solutions
generalized Tikhonov regularization
Mathematical analysis
Mathematical models
Regularization
space-fractional diffusion equation
spatial-dependent heat source
Tikhonov正则化方法
先验误差估计
分数阶扩散方程
未知源
空间
识别
连续依赖性
选择规则
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Summary: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.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(14)60065-5