4.3 Article

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

Journal

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
Volume 9, Issue 5, Pages 1801-1821

Publisher

WILMINGTON SCIENTIFIC PUBLISHER, LLC
DOI: 10.11948/20180318

Keywords

Inverse source problem; Tikhonov regularization; conjugate gradient algorithm

Funding

  1. NSF of China [11371181, 11771192]
  2. Institute of Scientific Computation and Financial data Analysis in Shanghai University of Finance and Economics

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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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