论文标题
schrödinger方程在没有几何控制条件的无界域上的可控性
Controllability of the Schrödinger equation on unbounded domains without geometric control condition
论文作者
论文摘要
我们在任何时候在$ \ mathbb {r}^d $中证明了schrödinger方程的可控性，任何时候$ t> 0 $，在非空，周期性的，开放式设置上支持内部控制。这特别表明，与波方程相比，全空间中Schrödinger方程的可控性具有更大的控制支持，并且表明，Schrödinger方程的全部空间控制理论可能更接近热方程的扩散性，而不是波动方程的弹道性质。我们的结果基于Floquet-Bloch理论与Ingham型型傅立叶傅里叶序列的估计的结合。
We prove controllability of the Schrödinger equation in $\mathbb{R}^d$ in any time $T > 0$ with internal control supported on nonempty, periodic, open sets. This demonstrates in particular that controllability of the Schrödinger equation in full space holds for a strictly larger class of control supports than for the wave equation and suggests that the control theory of Schrödinger equation in full space might be closer to the diffusive nature of the heat equation than to the ballistic nature of the wave equation. Our results are based on a combination of Floquet-Bloch theory with Ingham-type estimates on lacunary Fourier series.
