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arXiv · 2506.17648

Simultaneous Identification of Coefficients and Source in a Subdiffusion Equation from One Passive Measurement

Maolin Deng·Ali Feizmohammadi·Bangti Jin·Yavar Kian
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Abstract

This article is devoted to the detection of parameters in anomalous diffusion from a single passive measurement. More precisely, we consider the simultaneous identification of coefficients as well as a time-dependent source term appearing in a time-fractional diffusion equation from a single boundary or internal passive measurement. We obtain several uniqueness results in dimension one as well as a multidimensional extension under some symmetry assumptions. Our analysis relies on spectral representation of solutions, complex and harmonic analysis combined with some known inverse spectral results for Sturm-Liouville operators. The theoretical results are complemented by a corresponding reconstruction algorithm and numerical simulations.

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Maolin Deng, Ali Feizmohammadi, Bangti Jin, Yavar Kian. 2025-06-21. Simultaneous Identification of Coefficients and Source in a Subdiffusion Equation from One Passive Measurement. https://doi.org/10.1007/s00209-026-03998-6

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