Global Controllability of the Kawahara Equation at Any Time
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912152321785856 |
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| author | Ahamed, Sakil Mondal, Debanjit |
| author_facet | Ahamed, Sakil Mondal, Debanjit |
| contents | In this article, we prove that the nonlinear Kawahara equation on the periodic domain \(\mathbb{T}\) (the unit circle in the plane) is globally approximately controllable in \(H^s(\mathbb{T})\) for \(s \in \mathbb{N}\), at any time \(T > 0\), using a two-dimensional control force. The proof is based on the Agrachev-Sarychev approach in geometric control theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Controllability of the Kawahara Equation at Any Time Ahamed, Sakil Mondal, Debanjit Analysis of PDEs Optimization and Control In this article, we prove that the nonlinear Kawahara equation on the periodic domain \(\mathbb{T}\) (the unit circle in the plane) is globally approximately controllable in \(H^s(\mathbb{T})\) for \(s \in \mathbb{N}\), at any time \(T > 0\), using a two-dimensional control force. The proof is based on the Agrachev-Sarychev approach in geometric control theory. |
| title | Global Controllability of the Kawahara Equation at Any Time |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2412.08353 |