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Karine Beauchard; Camille Laurent
Local exact controllability of the $2$D-Schrödinger-Poisson system
(Contrôlabilité locale exacte du système de Schrödinger-Poisson 2D)
Journal de l'École polytechnique — Mathématiques, 4 (2017), p. 287-336, doi: 10.5802/jep.44
Article PDF | TeX source
Class. Math.: 35Q40, 35Q41, 93C10, 93C20
Mots clés: Contrôle d’équations aux dérivées partielles, système de Schrödinger-Poisson, contrôle bilinéaire

Résumé - Abstract

Dans cet article, nous étudions la contrôlabilité exacte du système de Schrödinger-Poisson 2D, qui couple une équation de Schrödinger sur un ouvert borné 2D, avec une équation de Poisson pour le potentiel électrique. Le contrôle agit sur le système via une condition de Neumann sur le potentiel, localement distribuée sur le bord du domaine spatial. Nous démontrons plusieurs résultats, avec ou sans non-linéarité, avec différents types de conditions de bord sur la fonction d’onde, de type Dirichlet ou de type Neumann.

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