We study the boundary controllability of a nonlinear Korteweg-de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
Cite this article
Jean-Michel Coron, Emmanuelle Crépeau, Exact boundary controllability of a nonlinear KdV equation with critical lengths. J. Eur. Math. Soc. 6 (2004), no. 3, pp. 367–398DOI 10.4171/JEMS/13