Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source
2020 ◽
Vol 28
(2)
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pp. 211-235
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A Priori
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AbstractIn this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.
2019 ◽
Vol 27
(5)
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pp. 609-621
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2019 ◽
Vol 38
(2)
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2011 ◽
Vol 14
(1)
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2019 ◽
Vol 34
(3)
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pp. 284-308
2019 ◽
Vol 349
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pp. 292-303
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