Exact controllability of the linear Zakharov-Kuznetsov equation

DOI10.3934/dcdsb.2020080zbMath1454.37073arXiv1912.03066OpenAlexW2991942418MaRDI QIDQ2211456

Mo Chen, Lionel Rosier

Publication date: 11 November 2020

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.03066

zbMATH Keywords

exact controllabilityGevrey functionsnull controllabilityZakharov-Kuznetsov equationreachable statesflatness approach

Mathematics Subject Classification ID

Controllability (93B05) KdV equations (Korteweg-de Vries equations) (35Q53) Dynamical systems in control (37N35) Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems (37K99) PDEs in connection with control and optimization (35Q93)

Related Items

Modified and subcritical Zakharov-Kuznetsov equations posed on rectangles ⋮ Modified Zakharov-Kuznetsov equation posed on a half-strip ⋮ Reachable states for the distributed control of the heat equation ⋮ Modified Zakharov–Kuznetsov equation posed on a strip ⋮ Exact Controllability and Stabilization for Linear Dispersive PDE’s on the Two-Dimensional Torus ⋮ Supercritical Zakharov-Kuznetsov equation posed on bounded rectangles

Cites Work

• Unnamed Item
• Control and stabilization of the Korteweg-de Vries equation: recent progresses
• An initial boundary-value problem for the Zakharov-Kuznetsov equation
• The Cauchy problem for the 3D Zakharov-Kuznetsov equation
• Initial-boundary value problems in a rectangle for two-dimensional Zakharov-Kuznetsov equation
• Exact controllability of semilinear heat equations in spaces of analytic functions
• Stabilization for the linear Zakharov-Kuznetsov equation without critical size restrictions
• Control of a Korteweg-de Vries equation: a tutorial
• An initial and boundary-value problem for the Zakharov-Kuznestov equation in a bounded domain
• Stabilization of Regular Solutions for the Zakharov-Kuznetsov Equation Posed on Bounded Rectangles and on a Strip
• Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
• Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit
• On the Reachable States for the Boundary Control of the Heat Equation
• Well-Posedness for the ZK Equation in a Cylinder and on the Background of a KdV Soliton
• Exact Controllability of a Linear Korteweg--de Vries Equation by the Flatness Approach
• Control of the surface of a fluid by a wavemaker