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arXiv · 2507.06524

Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion

Jiho Hong·Bangti Jin·Yavar Kian
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Abstract

In this work we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from the observation at one point on the boundary without / with the knowledge of medium properties, and a conditional Lipschitz stability estimate when the observation is available on the whole boundary. The analysis crucially employs resolvent estimates in the $L^r(\Omega)$ ($r>d$) spaces, solution representation in the Laplace domain and novel asymptotic expansions of the Laplace transform of the boundary flux at $p= 0$ and $p=1$.

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Jiho Hong, Bangti Jin, Yavar Kian. 2025-07-09. Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion. https://arxiv.org/abs/2507.06524

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