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Volume 9, Number 5, 2019, Pages 1801-1821                                                                DOI:10.11948/20180318
Recovering a space-dependent source term in a time-fractional diffusion wave equation
Ting Wei,Xiongbin Yan
Keywords:Inverse source problem, Tikhonov regularization, conjugate gradient algorithm.
      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.
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