Journal
INVERSE PROBLEMS
Volume 32, Issue 8, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/32/8/085003
Keywords
inverse source problem; fractional diffusion equation; conjugate gradient method
Categories
Funding
- NSF of China [11371181]
- Fundamental Research Funds for the Central Universities [lzujbky-2013-k02]
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This paper is devoted to identifying a time-dependent source term in a multidimensional time-fractional diffusion equation from boundary Cauchy data. The existence and uniqueness of a strong solution for the corresponding direct problem with homogeneous Neumann boundary condition are firstly proved. We provide the uniqueness and a stability estimate for the inverse time-dependent source problem. Then we use the Tikhonov regularization method to solve the inverse source problem and propose a conjugate gradient algorithm to find a good approximation to the minimizer of the Tikhonov regularization functional. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.
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