Control of the Schrödinger equation. (Contrôle de l’équation de Schrödinger.) (French) Zbl 0838.35013

Lebeau, G.

J. Math. Pures Appl., IX. Sér. 71, No. 3, 267-291 (1992).

The author extends the result on exact controllability for hyperbolic equations of C. Bardos, the author and J. Rauch [Appendix 2 in the book by J. L. Lions: Contrôlabilité exacte. Perturbations et stabilisations des systèmes distribués, Recherches en Mathématiques Appliquées 8 and 9 (Masson 1988; Zbl 0653.93002)] to the case of the evolution Schrödinger type equations, like for example the plate equation: \(\partial^2_t+ \Delta^2\). One of the ingredients in the proof is a semi-classical inequality in the spirit of Helffer-Sjöstrand.

Reviewer: B.Helffer (Orsay)

MSC:

35B37	PDE in connection with control problems (MSC2000)
35Q55	NLS equations (nonlinear Schrödinger equations)
93B05	Controllability

Keywords:

plate equation

Citations:

Zbl 0653.93002