Optimal control of a parabolic equation with a nonlocal nonlinearity
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911802028195840 |
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| author | Kenne, Cyrille Djomegne, Landry Mophou, Gisèle |
| author_facet | Kenne, Cyrille Djomegne, Landry Mophou, Gisèle |
| contents | This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain. We prove the existence and uniqueness of the solution to the system and the boundedness of the solution. Regularity results for the control-to-state operator, the cost functional and the adjoint state are also proved. We show the existence of optimal solutions and derive first-order necessary optimality conditions. In addition, second-order necessary and sufficient conditions for optimality are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14559 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal control of a parabolic equation with a nonlocal nonlinearity Kenne, Cyrille Djomegne, Landry Mophou, Gisèle Optimization and Control Analysis of PDEs 35K58, 49K20, 90C46, 92D25 This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain. We prove the existence and uniqueness of the solution to the system and the boundedness of the solution. Regularity results for the control-to-state operator, the cost functional and the adjoint state are also proved. We show the existence of optimal solutions and derive first-order necessary optimality conditions. In addition, second-order necessary and sufficient conditions for optimality are established. |
| title | Optimal control of a parabolic equation with a nonlocal nonlinearity |
| topic | Optimization and Control Analysis of PDEs 35K58, 49K20, 90C46, 92D25 |
| url | https://arxiv.org/abs/2306.14559 |