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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.25266 |
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| _version_ | 1866910173043359744 |
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| author | Janno, Jaan |
| author_facet | Janno, Jaan |
| contents | Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a boundary of the space domain is considered. Uniqueness for this problem is proved under the assumption that an order of a fractional derivative involved in the equation is irrational. The uniqueness result is generalized to an inverse problem for a coupled system of fractional diffusion equations, where both sources and initial states are unknown and first component of the state is measured on the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25266 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness of simultaneous reconstruction of general space- and time-dependent sources and initial states in fractional diffusion equations and systems from single boundary measurements Janno, Jaan Analysis of PDEs Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a boundary of the space domain is considered. Uniqueness for this problem is proved under the assumption that an order of a fractional derivative involved in the equation is irrational. The uniqueness result is generalized to an inverse problem for a coupled system of fractional diffusion equations, where both sources and initial states are unknown and first component of the state is measured on the boundary. |
| title | Uniqueness of simultaneous reconstruction of general space- and time-dependent sources and initial states in fractional diffusion equations and systems from single boundary measurements |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.25266 |