Exact controllability of the linear Zakharov-Kuznetsov equation

Mo Chen; Lionel Rosier

doi:10.3934/dcdsb.2020080

Article Contents

2020, Volume 25, Issue 10: 3889-3916. Doi: 10.3934/dcdsb.2020080

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Exact controllability of the linear Zakharov-Kuznetsov equation

Mo Chen^1, and
Lionel Rosier^2a,2b, ,

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
^* Corresponding author

Received: July 31, 2019

Early access: January 2020

Published: October 2020

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)

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Abstract

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.

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Mathematics Subject Classification: 37L50, 93B05.

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References

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