Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications

Nersesyan, Vahagn

Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 901-915 / Harvested from Numdam

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Résumé

We prove that the Schrödinger equation is approximately controllable in Sobolev spaces $H^{s}$ , $s > 0$ , generically with respect to the potential. We give two applications of this result. First, in the case of one space dimension, combining our result with a local exact controllability property, we get the global exact controllability of the system in higher Sobolev spaces. Then we prove that the Schrödinger equation with a potential which has a random time-dependent amplitude admits at most one stationary measure on the unit sphere S in $L^{2}$ .

Publié le : 2010-01-01

MR 2629885 | Zbl 1191.35257 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.anihpc.2010.01.004

@article{AIHPC_2010__27_3_901_0,
     author = {Nersesyan, Vahagn},
     title = {Global approximate controllability for Schr\"odinger equation in higher Sobolev norms and applications},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {27},
     year = {2010},
     pages = {901-915},
     doi = {10.1016/j.anihpc.2010.01.004},
     mrnumber = {2629885},
     zbl = {1191.35257},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2010__27_3_901_0}
}

Nersesyan, Vahagn. Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) pp. 901-915. doi : 10.1016/j.anihpc.2010.01.004. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_3_901_0/

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