Control and Stabilization of the Nonlinear Schroedinger Equation on RectanglesReport as inadecuate




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1 IECN - Institut Élie Cartan de Nancy 2 Department of Mathematical Sciences Cincinnati

Abstract : This paper studies the local exact controllability and the local stabilization of the semilinear Schrödinger equation posed on a product of $n$ intervals $n\ge 1$. Both internal and boundary controls are considered, and the results are given with periodic resp. Dirichlet or Neumann boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as far as the localization of the control region and the smoothness of the state space are concerned. It is also proved that for the linear Schrödinger equation with Dirichlet control, the exact controllability holds in $H^{-1}\Omega $ whenever the control region contains a neighborhood of a vertex.

Keywords : Schrodinger equation Bourgain spaces exact boundary controllability exact internal controllability exponential stabilization





Author: Lionel Rosier - Bing-Yu Zhang -

Source: https://hal.archives-ouvertes.fr/



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