Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit

Olivier Glass (1) , Sergio Guerrero (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper, we deal with controllability properties of linear and nonlinear Korteweg-de Vries equations in a bounded interval. First, we establish the null controllability of the linear equation via the left Dirichlet boundary condition, and its exact controllability via both Dirichlet boundary conditions. As a consequence, we obtain local exact controllability results for the nonlinear KdV equation. Finally, we prove a result of uniform controllability of the linear KdV equation in the limit of zero-dispersion.

Domaines: Analyse numérique [math.NA]

Olivier Glass, Sergio Guerrero. Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit. Asymptotic Analysis, 2008, 60, pp.61-100. ⟨hal-00139614⟩