Global exact controllability in infinite time of Schrödinger equation: multidimensional case

Vahagn Nersesyan (1) , Hayk Nersisyan (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We prove that the multidimensional Schrödinger equation is exactly controllable in infinite time near any point which is a finite linear combination of eigenfunctions of the Schrödinger operator. We prove that, generically with respect to the potential, the linearized system is controllable in infinite time. Applying the inverse mapping theorem, we prove the controllability of the nonlinear system.

Domaines: Equations aux dérivées partielles [math.AP]

Vahagn Nersesyan, Hayk Nersisyan. Global exact controllability in infinite time of Schrödinger equation: multidimensional case. Journal de Mathématiques Pures et Appliquées, 2012, 97 (4), pp.295-317. ⟨10.1016/j.matpur.2011.11.005⟩. ⟨hal-00660478⟩