On the optimality conditions for a fractional diffusive equation with a nonlocal term
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911057712250880 |
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| author | Gasimov, Jasarat Mahmudov, Nazim |
| author_facet | Gasimov, Jasarat Mahmudov, Nazim |
| contents | We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order $0 < s < 1$, incorporating a nonlocal time component modeled by an integral kernel. After establishing well-posedness of the problem, we analyze the properties of the control-to-state operator. We prove the existence of at least one optimal control and derive both first-order and second-order optimality conditions, which ensure local uniqueness. Under further assumptions, we also demonstrate that global uniqueness of the optimal control can be achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the optimality conditions for a fractional diffusive equation with a nonlocal term Gasimov, Jasarat Mahmudov, Nazim Optimization and Control We study a bilinear OCP for an evolution equation governed by the fractional Laplacian of order $0 < s < 1$, incorporating a nonlocal time component modeled by an integral kernel. After establishing well-posedness of the problem, we analyze the properties of the control-to-state operator. We prove the existence of at least one optimal control and derive both first-order and second-order optimality conditions, which ensure local uniqueness. Under further assumptions, we also demonstrate that global uniqueness of the optimal control can be achieved. |
| title | On the optimality conditions for a fractional diffusive equation with a nonlocal term |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.11058 |