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- W3170171749 abstract "Consider the recovery of the weight function in distributed time-fractional diffusion system using the interior measurement, which arises in some ultra-slow diffusion phenomena. Due to the nonlinear and nonlocal dependance of the measurement data on the weight function, such an inverse problem is novel and important. Based on the regularities of the direct problems for general diffusion equations with distributed time fractional derivative shown in this paper, we establish the theoretical framework for the optimization version of the inverse problem, including existence of the minimizer, the differentiability of the cost functional, as well as the gradient of the cost functional, in suitable functional spaces. Then an iteration process of descent type is realized efficiently for minimizing the regularizing cost functional in terms of the gradient type iteration, with numerical examples showing the validity of the proposed scheme." @default.
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- W3170171749 date "2021-10-01" @default.
- W3170171749 modified "2023-09-30" @default.
- W3170171749 title "Recovering the weight function in distributed order fractional equation from interior measurement" @default.
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- W3170171749 doi "https://doi.org/10.1016/j.apnum.2021.05.026" @default.
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