# American Institute of Mathematical Sciences

October  2020, 25(10): 3889-3916. doi: 10.3934/dcdsb.2020080

## Exact controllability of the linear Zakharov-Kuznetsov equation

 1. School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, China 2a. TAG_SUP Université du Littoral Côte d'Opale, Laboratoire de Mathématiques Pures et Appliquées J. Liouville, BP 699, F-62228 Calais, France 2b. TAG_SUP CNRS FR 2956, France

* Corresponding author

Received  August 2019 Published  October 2020 Early access  January 2020

Fund Project: The first author (MC) is supported by NSFC Grant (11701078) and China Scholarship Council. The second author (LR) is supported by the ANR project Finite4SoS (ANR-15-CE23-0007)

We consider the linear Zakharov-Kuznetsov equation on a rectangle with a left Dirichlet boundary control. Using the flatness approach, we prove the null controllability of that equation and provide a space of analytic reachable states.

Citation: Mo Chen, Lionel Rosier. Exact controllability of the linear Zakharov-Kuznetsov equation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3889-3916. doi: 10.3934/dcdsb.2020080
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