An inverse problem for space‐fractional backward diffusion problem |
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Authors: | Jingjun Zhao Songshu Liu Tao Liu |
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Institution: | Department of Mathematics, Harbin Institute of Technology, , Harbin, 150001 China |
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Abstract: | In this paper, an inverse problem for space‐fractional backward diffusion equation, which is highly ill‐posed, is considered. This problem is obtained from the classical diffusion equation by replacing the second‐order space derivative with a Riesz–Feller derivative of order α ∈ (0,2]. We show that such a problem is severely ill‐posed, and further present a simplified Tikhonov regularization method to deal with this problem. Convergence estimate is presented under a priori choice of regularization parameter. Numerical experiments are given to illustrate the accuracy and efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | ill‐posed problems inverse problems regularization method fractional backward diffusion problem |
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