Exact boundary controllability of the nonlinear Schrödinger equation
Résumé
This paper studies the exact boundary controllability of the semilinear Schrödinger equation posed on a bounded domain Ω ⊂ Rn with either the Dirichlet boundary conditions or the Neumann boundary conditions. It is shown that if s > n/2, or 0 ≤ s < n/2 with 1 ≤ n < 2+2s, or s = 0,1 with n = 2, then the systems are locally exactly controllable in the classical Sobolev space Hs(Ω) around any smooth solution of the cubic Schrödinger equation.