| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 75 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/cocv/2019062 | |
| Published online | 30 September 2020 | |
Internal null controllability of the generalized Hirota-Satsuma system*
1
Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V,
Valparaíso, Chile.
2
Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK,
38000
Grenoble, France.
** Corresponding author: emmanuelle.crepeau@univ-grenoble-alpes.fr
Received:
5
April
2019
Accepted:
7
October
2019
The generalized Hirota-Satsuma system consists of three coupled nonlinear Korteweg-de Vries (KdV) equations. By using two distributed controls it is proven in this paper that the local null controllability property holds when the system is posed on a bounded interval. First, the system is linearized around the origin obtaining two decoupled subsystems of third order dispersive equations. This linear system is controlled with two inputs, which is optimal. This is done with a duality approach and some appropriate Carleman estimates. Then, by means of an inverse function theorem, the local null controllability of the nonlinear system is proven.
Mathematics Subject Classification: 35Q35 / 93B05 / 93C20 / 93C10
Key words: Korteweg-de Vries equation / null controllability / Carleman estimates
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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