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Determination of the initial data in a time-fractional diffusion-wave problem by a final time data.
- Source :
-
Computers & Mathematics with Applications . Oct2019, Vol. 78 Issue 8, p2525-2540. 16p. - Publication Year :
- 2019
-
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]
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 78
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 138523144
- Full Text :
- https://doi.org/10.1016/j.camwa.2019.03.056