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- W4299587868 abstract "We consider the 1D linear Schr{o}dinger equation, on a bounded interval, with Dirichlet boundary conditions and bilinear scalar control. The small-time local exact controllability around the ground state was proved in [BeaLau10], under an appropriate nondegeneracy assumption. Here, we work under a weaker nondegeneracy assumption and we prove the small-time local exact controllability in projection, around the ground state, with estimates on the control (depending linearly on the target) simultaneously in several spaces. These estimates are obtained at the level of the linearized system, thanks to a new result about trigonometric moment problems. Then, they are transported to the nonlinear system by the inverse mapping theorem, thanks to appropriate estimates of the error between the nonlinear and the linearized dynamics." @default.
- W4299587868 created "2022-10-02" @default.
- W4299587868 creator A5039119960 @default.
- W4299587868 date "2021-07-19" @default.
- W4299587868 modified "2023-09-27" @default.
- W4299587868 title "Local controllability of the bilinear 1D Schr{o}dinger equation with simultaneous estimates" @default.
- W4299587868 doi "https://doi.org/10.48550/arxiv.2107.08817" @default.
- W4299587868 hasPublicationYear "2021" @default.
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