Maolin Deng, Ali Feizmohammadi, Bangti Jin, Yavar Kian
Published 2025-06-21Version 1
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.
Analytical solutions of moving boundary problems for the time-fractional diffusion equation
$L^p$ estimates for wave equations with specific $C^{0,1}$ coefficients
On the well-posedness of the time-fractional diffusion equation with Robin boundary condition
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