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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.10315 |
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| _version_ | 1866918091156357120 |
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| author | Creo, Simone Lancia, Maria Rosaria Mola, Andrea Mola, Gianluca Romanelli, Silvia |
| author_facet | Creo, Simone Lancia, Maria Rosaria Mola, Andrea Mola, Gianluca Romanelli, Silvia |
| contents | 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 $α$ 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 $α\to 1^{-}$, the solution corresponding to $α$ tends to the classical one ($α=1$). Applications to examples of heat diffusion and elasticity are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identification problems for anisotropic time-fractional subdiffusion equations Creo, Simone Lancia, Maria Rosaria Mola, Andrea Mola, Gianluca Romanelli, Silvia Analysis of PDEs 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 $α$ 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 $α\to 1^{-}$, the solution corresponding to $α$ tends to the classical one ($α=1$). Applications to examples of heat diffusion and elasticity are presented. |
| title | Identification problems for anisotropic time-fractional subdiffusion equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.10315 |