1. Determination of the initial data in a time-fractional diffusion-wave problem by a final time data.
- Author
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Xian, J. and Wei, T.
- Subjects
- *
TIKHONOV regularization , *SEPARATION of variables , *ADJOINT differential equations , *WAVE equation , *INITIAL value problems , *CONJUGATE gradient methods - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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