Exact controllability of the linear Zakharov-Kuznetsov equation
Mo Chen, Lionel Rosier (LMPA)
TL;DR
This paper proves the exact null controllability of the linear Zakharov-Kuznetsov equation on a rectangle using the flatness approach, and characterizes the space of states that can be reached.
Contribution
It introduces a novel application of the flatness approach to achieve controllability results for the Zakharov-Kuznetsov equation.
Findings
Null controllability is achieved with boundary control.
A space of analytic reachable states is characterized.
The flatness approach is effectively applied to a PDE control problem.
Abstract
We consider the linear Zakharov-Kuznetsov equation on a rectangle with a left Dirich-let boundary control. Using the flatness approach, we prove the null controllability of this equation and provide a space of analytic reachable states.
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