Bilinear optimal control for a fractional diffusive equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909400230264832 |
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| author | Mophou, Gisèle Kenne, Cyrille Warma, Mahamadi |
| author_facet | Mophou, Gisèle Kenne, Cyrille Warma, Mahamadi |
| contents | We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some weak maximum principle results allowing us to obtain more regularity of our state equation. Then, we consider an optimal control problem which consists to bring the state of the system at final time to a desired state. We show that this optimal control problem has a solution and we derive the first and second order optimality conditions. Finally, under additional assumptions on the initial datum and the given target, we prove that local uniqueness of optimal solutions can be achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_17494 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bilinear optimal control for a fractional diffusive equation Mophou, Gisèle Kenne, Cyrille Warma, Mahamadi Optimization and Control Analysis of PDEs We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some weak maximum principle results allowing us to obtain more regularity of our state equation. Then, we consider an optimal control problem which consists to bring the state of the system at final time to a desired state. We show that this optimal control problem has a solution and we derive the first and second order optimality conditions. Finally, under additional assumptions on the initial datum and the given target, we prove that local uniqueness of optimal solutions can be achieved. |
| title | Bilinear optimal control for a fractional diffusive equation |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2210.17494 |