Local exact controllability of the 2D-Schrödinger-Poisson system

Karine Beauchard (1, 2) , Camille Laurent (3)

1 ENS Rennes - École normale supérieure - Rennes
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 LJLL - Laboratoire Jacques-Louis Lions

In this article, we investigate the exact controllability of the 2D-Schrödinger-Poisson system, which couples a Schrödinger equation on a bounded domain of R 2 with a Poisson equation for the electrical potential. The control acts on the system through a Neumann boundary condition on the potential, locally distributed on the boundary of the space domain. We prove several results, with or without nonlinearity and with dierent boundary conditions on the wave function, of Dirichlet type or of Neumann type.

Mots clés: contrôle d'équations aux dérivées partielles; systèmes de Schrödinger-Poisson; contôle bilinéaire

Domaines: Mathématiques [math]

Karine Beauchard, Camille Laurent. Local exact controllability of the 2D-Schrödinger-Poisson system. Journal de l'École polytechnique — Mathématiques, 2017, 4, pp.287-336. ⟨10.5802/jep.44⟩. ⟨hal-01333627⟩