Controllability of a quantum particle in a moving potential well

Journal of Functional Analysis

Volumn 232, Issue 2, 2006, Pages 328-389

  Beauchard, Karine ^a   Coron, Jean Michel ^a,b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Controllability; Nash Moser; Schr dinger

Indexed keywords

EID: 31744450577     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2005.03.021     Document Type: Article

References (18)

1. K. Beauchard, Local controllability of a 1-D Schrödinger equation, Prépubl. Univ. Paris Sud, (accepted in Journal de Mathématiques Pures et Appliquées), 2004.
2. J.-M. Coron Global asymptotic stabilization for controllable systems without drift Math. Control Signals Systems 5 1992 295-312
3. J.-M. Coron Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels C.R. Acad. Sci. Paris 317 1993 271-276
4. J.-M. Coron On the controllability of 2-D incompressible perfect fluids J. Math. Pures Appl. 75 1996 155-188
5. J.-M. Coron On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions ESAIM: COCV 1 1996 35-75
6. J.-M. Coron Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations ESAIM: COCV 8 2002 513-554
7. J.-M. Coron E. Crépeau Exact boundary controllability of a nonlinear KdV equation with critical lengths J. European Math. Soc. 6 2004 367-398
8. J.-M. Coron A. Fursikov Global exact controllability of the 2-D Navier-Stokes equations on a manifold without boundary Russian Journal of Mathematical Physics 4 1996 429-448
9. A.V. Fursikov, O.Yu. Imanuvilov, Exact controllability of the Navier-Stokes and Boussinesq equations, Russian Math. Surveys 54 (3) (1999) 565-618; Uspekhi Mat. Nauk 54 (3) (1999) 565-618 (in Russian).
10. O. Glass Exact boundary controllability of 3-D Euler equation ESAIM: COCV 5 2000 1-44
11. O. Glass On the controllability of the Vlasov-Poisson system Journal of Differential Equations 195 2003 332-379
12. G. Gromov Partial Differential Relations 1986 Springer Berlin, New York, London
13. L. Hörmander On the Nash-Moser implicit function theorem Ann. Acad. Sci. Fennicae 1985 255-259
14. Th. Horsin On the controllability of the Burgers equation ESAIM: COCV 3 1998 83-95
15. T. Kato Perturbation Theory for Linear operators 1966 Springer Berlin, New York
16. P. Rouchon, Control of a quantum particule in a moving potential well, Second IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Seville, 2003.
17. E. Zuazua, Remarks on the controllability of the Schrödinger equation, CRM Proceedings and Lecture Notes, vol. 33, 2003.
18. G. Turinici, On the controllability of bilinear quantum systems, in: M. Defranceschi, C. Le Bris (Eds.), Mathematical models and methods for ab initio quantum chemistry. Lecture Notes in Chem. Vol. 74, Springer, Berlin, 2000, pp. 75-92.