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arXiv · 2610.33896

Recovery of a source of anomalous diffusion from space-time sparse data

Xing Cheng·Bangti Jin·Yavar Kian·Zhiyuan Li
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Abstract

We study an inverse source problem for a time-fractional sub- and super-diffusive anomalous diffusion equation on the unit disk with sparse boundary observations. We prove the recovery of a general class of $L^2$ sources for anomalous diffusion, with separated variables, from boundary measurements that are sparse in both space and time, using observations at two carefully chosen boundary points on a discrete set of times arbitrarily close to the final time. The analysis relies heavily on the memory effect of the model, properties of complex analysis and the representation of solutions.

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Xing Cheng, Bangti Jin, Yavar Kian, Zhiyuan Li. 2026-10-24. Recovery of a source of anomalous diffusion from space-time sparse data. https://arxiv.org/abs/2610.33896

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