Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.33896

Authors: Cheng, Xing, Jin, Bangti, Kian, Yavar, Li, Zhiyuan

Institutions: Hohai University, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques Raphaël Salem, Université de Rouen Normandie, Ningbo University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Agence Nationale de la Recherche, National Natural Science Foundation of China, Government of Jiangsu Province

Awards: G1920647447, Parameter identifications for anomalous diffusion, G2382013997, G6227346462, G6856721283, G8446722958, G8478990708

OpenAlex ID: W7223807374

Cites: 1

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