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

Nersesyan, Vahagn

doi:10.1016/j.anihpc.2010.01.004

Nersesyan, Vahagn

Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 27 (2010) no. 3, pp. 901-915

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 $L^{2}$ .

MR Zbl

DOI : 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'Institut Henri Poincar\'e. C, Analyse non lin\'eaire},
     pages = {901--915},
     year = {2010},
     publisher = {Elsevier},
     volume = {27},
     number = {3},
     doi = {10.1016/j.anihpc.2010.01.004},
     mrnumber = {2629885},
     zbl = {1191.35257},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2010.01.004/}
}

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Nersesyan, Vahagn. Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications. Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 27 (2010) no. 3, pp. 901-915. doi: 10.1016/j.anihpc.2010.01.004

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