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• W2051216605 endingPage "065014" @default.
• W2051216605 startingPage "065014" @default.
• W2051216605 abstract "This paper deals with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the fractional order in the 1D timefractional diffusion equation with smooth initial functions by using boundary measurements. The uniqueness results for the inverse problem are proved on the basis of the inverse eigenvalue problem, and the Lipschitz continuity of the solution operator is established. A modified optimal perturbation algorithm with a regularization parameter chosen by a sigmoid-type function is put forward for the discretization of the minimization problem. Numerical inversions are performed for the diffusion coefficient taking on different functional forms and the additional data having random noise. Several factors which have important influences on the realization of the algorithm are discussed, including the approximate space of the diffusion coefficient, the regularization parameter and the initial iteration. The inversion solutions are good approximations to the exact solutions with stability and adaptivity demonstrating that the optimal perturbation algorithm with the sigmoid-type regularization parameter is efficient for the simultaneous inversion. (Some figures may appear in colour only in the online journal)" @default.
• W2051216605 created "2016-06-24" @default.
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• W2051216605 date "2013-05-16" @default.
• W2051216605 modified "2023-10-12" @default.
• W2051216605 title "Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation" @default.
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• W2051216605 doi "https://doi.org/10.1088/0266-5611/29/6/065014" @default.
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