Linear Test Approach to Global Controllability of Higher-Order Nonlinear Dispersive Equations with Finite-Dimensional Control
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909591894228992 |
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| author | Mondal, Debanjit |
| author_facet | Mondal, Debanjit |
| contents | We investigate a class of higher-order nonlinear dispersive equations posed on the circle, subject to additive forcing by a finite-dimensional control. Our main objective is to establish approximate controllability by using the controllability of the inviscid Burgers system, linearized around a suitably constructed trajectory. In contrast to earlier approaches based on Lie algebraic techniques, our method offers a more concise proof and sheds new light on the structure of the control. Although the approach necessitates a higher-dimensional control space, both the structure and dimension of the control remain uniform with respect to the order of the dispersive equation and the control time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Test Approach to Global Controllability of Higher-Order Nonlinear Dispersive Equations with Finite-Dimensional Control Mondal, Debanjit Analysis of PDEs Optimization and Control 35Q31, 35Q35, 35Q53, 93B05, 93B18 We investigate a class of higher-order nonlinear dispersive equations posed on the circle, subject to additive forcing by a finite-dimensional control. Our main objective is to establish approximate controllability by using the controllability of the inviscid Burgers system, linearized around a suitably constructed trajectory. In contrast to earlier approaches based on Lie algebraic techniques, our method offers a more concise proof and sheds new light on the structure of the control. Although the approach necessitates a higher-dimensional control space, both the structure and dimension of the control remain uniform with respect to the order of the dispersive equation and the control time. |
| title | Linear Test Approach to Global Controllability of Higher-Order Nonlinear Dispersive Equations with Finite-Dimensional Control |
| topic | Analysis of PDEs Optimization and Control 35Q31, 35Q35, 35Q53, 93B05, 93B18 |
| url | https://arxiv.org/abs/2504.17580 |