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Identification of a Spatially-Dependent Variable Order in One-Dimensional Subdiffusion
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abstract
In this work we investigate an inverse problem of identifying a spatially variable order in the one-dimensional subdiffusion model from the boundary flux measurement. The model involves a generalized Caputo derivative in time, and arises in the mathematical modeling of anomalous diffusion in heterogeneous media. We prove the unique recovery of a monotone piecewise constant variable order and its range for known and unknown media, respectively. The analysis is based on a delicate asymptotic expansion of the Laplace transform of the data as $p\to0$, which is of independent interest.
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Cited by 1 Pith paper
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Inverse source problem of sub-diffusion of variable exponent
For a time-fractional diffusion model with time-dependent order alpha(t), the space-dependent source is claimed to be uniquely determined by local interior or boundary observations, with Lipschitz stability in a weak norm.
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