Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 78, Issue 8, Pages 2525-2540Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2019.03.056
Keywords
Inverse initial value problem; Fractional diffusion wave equation; Tikhonov regularization; Variational method; Conjugate gradient method
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Funding
- NSF of China [11371181, 11771192]
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This paper is to determine an initial value for a time-fractional diffusion-wave equation from the final time data. The regularity of the weak solution for the direct problem is improved. The existence and uniqueness of a weak solution for the adjoint problem are proved by using the Fourier method. The Tikhonov regularization method is applied for finding a stable approximate solution. In order to get the minimizer of the Tikhonov regularization functional, we propose a conjugate gradient algorithm based on the strict deductions of the sensitive problem and the adjoint problem. Four numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness and stability of the proposed algorithm. (C) 2019 Elsevier Ltd. All rights reserved.
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