Second-order optimality conditions for the bilinear optimal control of a degenerate equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909378424078336 |
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| author | Kenne, Cyrille Djomegne, Landry Zongo, Pascal |
| author_facet | Kenne, Cyrille Djomegne, Landry Zongo, Pascal |
| contents | The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of the state equation, as well as weak maximum principles are established. We prove some differentiability properties of the control-to-state operator and the existence of optimal solutions. Finally, we derive first- and second-order optimality conditions for the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11046 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Second-order optimality conditions for the bilinear optimal control of a degenerate equation Kenne, Cyrille Djomegne, Landry Zongo, Pascal Optimization and Control Analysis of PDEs 35B50, 35K65, 35Q93, 49J20, 49K20 The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of the state equation, as well as weak maximum principles are established. We prove some differentiability properties of the control-to-state operator and the existence of optimal solutions. Finally, we derive first- and second-order optimality conditions for the system. |
| title | Second-order optimality conditions for the bilinear optimal control of a degenerate equation |
| topic | Optimization and Control Analysis of PDEs 35B50, 35K65, 35Q93, 49J20, 49K20 |
| url | https://arxiv.org/abs/2212.11046 |