JournalsjemsVol. 6 , No. 3DOI 10.4171/jems/13

Exact boundary controllability of a nonlinear KdV equation with critical lengths

  • Jean-Michel Coron

    Université Pierre et Marie Curie, Paris, France
  • Emmanuelle Crépeau

    INRIA, Le Chesnay, France
Exact boundary controllability of a nonlinear KdV equation with critical lengths cover

Abstract

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.