Exact boundary controllability of a nonlinear KdV equation with critical lengths

By Jean-Michel Coron, Emmanuelle Crépeau. 2004

166 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1bd06a33fd563153a529f4d5fe21b2d33bfaca78

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In Control and Systems Engineering

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Null controllability and stabilization of the linear Kuramoto-Sivashinsky equation (2009, methodology): “Thus, by applying Corollary 3.2 in [11], one gets Theorem 1.1.”
Control of a Korteweg-de Vries equation: A tutorial (2013, unknown): “[18, 7, 9] For any L ∈ N there exists TL > 0 such that for any T > TL, there exists r > 0 such that for every (y0, yT ) ∈ L(2)(0, L)(2) with ‖y0‖L2(0,L) < r and ‖yT ‖L2(0,L) < r, there exist h ∈ L(2)(0, T ) and y ∈ C([0, T ], L(2)(0, L)) ∩ L(2)(0, T,H(1)(0, L)) satisfying (1), y(0, ·) = y0 and y(T, ”
Controllability and asymptotic stabilization of the Camassa–Holm equation (2008, methodology): “Finally, concerning the controllability of other equations modelling surface water waves, let us mention [1, 12, 13, 28, 29, 30, 32, 34] for what concerns the Korteweg-de Vries equation, [26] for the linearized Benjamin-Bona-Mahony equation and [25] for the linearized Benjamin-Ono equation.”
CONTROL AND STABILIZATION OF A FAMILY OF BOUSSINESQ SYSTEMS (2009, methodology): “Rosier showed that the associated linear system is exactly controllable in the space L2(0, L) using the Hilbert Uniqueness Method (HUM), and that the nonlinear system is locally exactly controllable in the space L2(0, L). Interestingly, while Rosier showed in [31] that the linear system associated t”
Local rapid stabilization for a Korteweg–de Vries equation with a Neumann boundary control on the right (2013, background): “In [9], the term ∫ t 0 |h̃(s) − ĥ(s)|2 ds in the right hand side of (A.”
Controllability of a quantum particle in a moving potential well (2006, methodology): “It has already been used for an infinite-dimensional one, the Korteweg–de Vries equation, in [7].”
Local exact controllability to the trajectories of the 1-D Kuramoto–Sivashinsky equation☆ (2011, background): “Later, in [8,3,5] the authors proved that the KdV equation is exactly controllable in despite of the lack of this property for the linearized system.”
Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain (2009, methodology): “The proof of P (T ) given in [11] requires that the subspace M is one-dimensional, but this is not implied by the fact that L = 2kπ for some k ∈ N∗.”