Variational method for a backward problem for a time-fractional diffusion equation
2019 ◽
Vol 53
(4)
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pp. 1223-1244
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Keyword(s):
This paper is devoted to solve a backward problem for a time-fractional diffusion equation by a variational method. The regularity of a weak solution for the direct problem as well as the existence and uniqueness of a weak solution for the adjoint problem are proved. We formulate the backward problem into a variational problem by using the Tikhonov regularization method, and obtain an approximation to the minimizer of the variational problem by using a conjugate gradient method. Four numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed algorithm.
2017 ◽
Vol 97
(5)
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pp. 842-863
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Vol 27
(1)
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pp. 1-16
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Vol 37
(18-19)
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pp. 8518-8532
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2018 ◽
Vol 148
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pp. 37-47
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Vol 34
(3)
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pp. 284-308
2019 ◽
Vol 349
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pp. 292-303
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2020 ◽
Vol 97
(11)
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pp. 2375-2393
2015 ◽
Vol 279
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pp. 277-292
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2010 ◽
Vol 8
(5)
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pp. 1016-1051
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