Optimal bounds for the cost of fast controls of a KdV system
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915796513456128 |
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| author | Nguyen, Hoai-Minh |
| author_facet | Nguyen, Hoai-Minh |
| contents | We study the cost of fast controls for a linearized KdV system and a nonlinear KdV system locally, using right Neumann boundary control for non-critical lengths. Since the operator associated with the linearized system is neither self-adjoint nor skew-adjoint, its (known) spectral properties are not directly amenable to the moment method, leaving optimal cost bounds an open problem. We address this difficulty by shifting attention to a related KdV system and deriving the optimal bounds from the new one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12698 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal bounds for the cost of fast controls of a KdV system Nguyen, Hoai-Minh Optimization and Control Analysis of PDEs 93B05, 93C20, 35B40, 35Q53 We study the cost of fast controls for a linearized KdV system and a nonlinear KdV system locally, using right Neumann boundary control for non-critical lengths. Since the operator associated with the linearized system is neither self-adjoint nor skew-adjoint, its (known) spectral properties are not directly amenable to the moment method, leaving optimal cost bounds an open problem. We address this difficulty by shifting attention to a related KdV system and deriving the optimal bounds from the new one. |
| title | Optimal bounds for the cost of fast controls of a KdV system |
| topic | Optimization and Control Analysis of PDEs 93B05, 93C20, 35B40, 35Q53 |
| url | https://arxiv.org/abs/2602.12698 |