论文标题
紧凑型歧管上的分数Schrödinger方程：全局可控性结果
The fractional Schrödinger equation on compact manifolds: Global controllability results
论文作者
论文摘要
这项工作的目的是证明在$ d $二维紧凑的Riemannian歧管上，没有边界$（m，g）$上的分数Schrödinger方程的全球可控性和稳定性。为了证明我们的主要结果，我们在流形上使用伪差分计算的技术。更确切地说，通过使用微局部分析，我们能够证明规律性的传播，这些定期性与所谓的几何控制条件和独特的延续性属性一起，有助于我们证明正在考虑的系统为全球控制结果。作为主要新颖性，该手稿介绍了几何控制条件与分数Schrödinger方程的可控性之间的关系。
The goal of this work is to prove global controllability and stabilization properties for the fractional Schrödinger equation on $d$-dimensional compact Riemannian manifolds without boundary $(M,g)$. To prove our main results we use techniques of pseudo-differential calculus on manifolds. More precisely, by using microlocal analysis, we are able to prove propagation of regularity which together with the so-called Geometric Control Condition and Unique Continuation Property help us to prove global control results for the system under consideration. As a main novelty this manuscript presents the relation between the geometric control condition and the controllability for the fractional Schrödinger equation.
