On a final value problem for the time-fractional diffusion equation with inhomogeneous source |
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| Authors: | Nguyen Huy Tuan Le Dinh Long Van Thinh Nguyen Thanh Tran |
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| Affiliation: | 1. Department of Mathematics and Computer Science, University of Science, Viet Nam National University, Ho Chi Minh City, Vietnam.;2. Institute of Computational Science and Technology, Ho Chi Minh City, Vietnam.;3. Department of Civil and Environmental Engineering, Seoul National University, Seoul, Republic of Korea.;4. School of Mathematics and Statistics, The University of New South Wales, Sydney, Australia. |
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| Abstract: | In this paper, we consider an inverse problem for the time-fractional diffusion equation with inhomogeneous source to determine an initial data from the observation data provided at a later time. In general, this problem is ill-posed, therefore we construct a regularizing solution using the quasi-boundary value method. We also proposed both parameter choice rule methods, the a-priori and the a-posteriori methods, to estimate the convergence rate of the regularized methods. In addition, the proposed regularized methods have been verified by numerical experiments, and a comparison of the convergence rate between the a-priori and the a-posteriori choice rule methods is also given. |
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| Keywords: | Diffusion process fractional derivative backward problem regularization inhomogeneous source |
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