A modified regularized algorithm for a semilinear space‐fractional backward diffusion problem |
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| Authors: | Xiaoying Jiang Dinghua Xu Qifeng Zhang |
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| Institution: | 1. Department of Mathematics, College of Sciences, Zhejiang Sci‐Tech University, Hangzhou, Zhejiang, China;2. School of Mathematics, Shanghai University of Finance and Economics, Shanghai, China |
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| Abstract: | In this paper, we investigate a backward problem for a space‐fractional partial differential equation. The main purpose is to propose a modified regularization method for the inverse problem. The existence and the uniqueness for the modified regularized solution are proved. To derive the gradient of the optimization functional, the variational adjoint method is introduced, and hence, the unknown initial value is reconstructed. Finally, numerical examples are provided to show the effectiveness of the proposed algorithm. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | backward diffusion problem space‐fractional equations modified regularization variational adjoint method |
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