Recovering the initial distribution for space-fractional diffusion equation by a logarithmic regularization method |
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| Institution: | 1. College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan Province, PR China;2. Department of Mathematics, Luoyang Normal University, Luoyang, Henan 471022, PR China |
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| Abstract: | In this paper, the backward problem for space-fractional diffusion equation is investigated. We proposed a so-called logarithmic regularization method to solve it. Based on the conditional stability and an a posteriori regularization parameter choice rule, the convergence rate estimates are given under a-priori bound assumption for the exact solution. |
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| Keywords: | Backward problem Logarithmic regularization method Space-fractional diffusion equation Fractional Laplacian Convergence rate |
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