矩形域上非线性Schroedinger方程的控制与镇定
Control and Stabilization of the Nonlinear Schroedinger Equation on Rectangles
摘要：
研究了$n$区间乘积（$n\ge 1$）上半线性薛定谔方程的局部精确能控性和局部镇定性.同时考虑了内部控制和边界控制，并给出了周期控制的结果。Dirichlet或Neumann）边界条件。在内部控制的情况下，我们得到的局部可控性结果是尖锐的，就控制区域的局部化和状态空间的光滑性而言。证明了具有Dirichlet控制的线性薛定谔方程，只要控制区域包含一个顶点的邻域，精确能控性在$H^{-1}(Ω)$中成立.
英文摘要：
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 $H^{-1}(Ω)$ whenever the control region contains a neighborhood of a vertex.
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