RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION

Ting Wei; Xiongbin Yan

doi:10.11948/20180318

2019 Volume 9 Issue 5

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Ting Wei, Xiongbin Yan. RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1801-1821. doi: 10.11948/20180318

Citation:

Ting Wei, Xiongbin Yan. RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1801-1821. doi: 10.11948/20180318

RECOVERING A SPACE-DEPENDENT SOURCE TERM IN A TIME-FRACTIONAL DIFFUSION WAVE EQUATION

Ting Wei^1, ,,
Xiongbin Yan¹

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730030

Corresponding author: Email address:tingwei@lzu.edu.cn(T. Wei)
Fund Project: This work is supported by the NSF of China (11371181, 11771192) and by Institute of Scientific Computation and Financial data Analysis in Shanghai University of Finance and Economics

Abstract

Abstract

This work is concerned with identifying a space-dependent source function from noisy final time measured data in a time-fractional diffusion wave equation by a variational regularization approach. We provide a regularity of direct problem as well as the existence and uniqueness of adjoint problem. The uniqueness of the inverse source problem is discussed. Using the Tikhonov regularization method, the inverse source problem is formulated into a variational problem and a conjugate gradient algorithm is proposed to solve it. The efficiency and robust of the proposed method are supported by some numerical experiments.
- Inverse source problem /
- Tikhonov regularization /
- conjugate gradient algorithm
MSC: 65M32, 35R11

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References

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