Boundary controllability for the semilinear Schrodinger equations on Riemannian manifolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:372

Article

Deng, Li^1,2  Yao, Peng-Fei² 

[1] SW Jiaotong Univ, Dept Math, Inst Appl Math, Chengdu 610031, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Control & Syst, Beijing 100190, Peoples R China

关键词: Semilinear Schrodinger equation;    Exact controllability;    Riemannian metric;   

DOI  :  10.1016/j.jmaa.2010.06.043

来源: Elsevier

【 摘 要 】

We study the boundary exact controllability for the semilinear Schrodinger equation defined on an open, bounded, connected set Omega of a complete, n-dimensional, Riemannian manifold M with metric g. We prove the locally exact controllability around the equilibria under some checkable geometrical conditions. Our results show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and equilibria of the semilinear Schrodinger equation. We then establish the globally exact controllability in such a way that the state of the semilinear Schrodinger equation moves from an equilibrium in one location to an equilibrium in another location. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free