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

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

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