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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2401.10551 |
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| _version_ | 1866909077255225344 |
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| author | Li, Yating Zhang, Muming |
| author_facet | Li, Yating Zhang, Muming |
| contents | In this paper, we obtain a null controllability result for a coupled fourth order parabolic system based on the Stackelberg-Nash strategies. For this purpose, we first prove the existence and uniqueness of Nash equilibrium pair of the original system and its explicit expression is provided. Next, we investigate the null controllability of Nash equilibrium to the corresponding optimal system. By duality theory, we establish an observability estimate for the coupled fourth order parabolic system. Such an estimate is obtained by a new global Carleman estimate we derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hierarchic control for the coupled fourth order parabolic equations Li, Yating Zhang, Muming Optimization and Control In this paper, we obtain a null controllability result for a coupled fourth order parabolic system based on the Stackelberg-Nash strategies. For this purpose, we first prove the existence and uniqueness of Nash equilibrium pair of the original system and its explicit expression is provided. Next, we investigate the null controllability of Nash equilibrium to the corresponding optimal system. By duality theory, we establish an observability estimate for the coupled fourth order parabolic system. Such an estimate is obtained by a new global Carleman estimate we derived. |
| title | Hierarchic control for the coupled fourth order parabolic equations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.10551 |