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arXiv · 2507.10315

Identification problems for anisotropic time-fractional subdiffusion equations

Simone Creo·Maria Rosaria Lancia·Andrea Mola·Gianluca Mola·Silvia Romanelli
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Abstract

We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under energy-type overdeterminating conditions. We prove the uniqueness of the solution to the inverse problem when the fractional order $\alpha$ of the derivative is in $(0,1)$. A conditioned existence result is also provided, complemented with a suitable selection of numerical calculations. In addition, we prove that, as $\alpha\to 1^{-}$, the solution corresponding to $\alpha$ tends to the classical one ($\alpha=1$). Applications to examples of heat diffusion and elasticity are presented.

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Simone Creo, Maria Rosaria Lancia, Andrea Mola, Gianluca Mola, Silvia Romanelli. 2025-07-14. Identification problems for anisotropic time-fractional subdiffusion equations. https://arxiv.org/abs/2507.10315

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