Exact boundary controllability of the nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: Exact boundary controllability of the nonlinear Schrödinger equation
zbMATH Open document ID: 1171.35015
author: Lionel Rosier
author: Bing-Yu Zhang
published in: Journal of Differential Equations
publication date: 2009-05-19T00:00:00Z
review text: The paper deals with the problem of exact boundary controllability of the semilinear Schrödinger equation posed on a bounded domain \(\Omega\in\mathbb{R}^n\) with either the Dirichlet boundary conditions or the Neumann boundary conditions. The authors establish interrelation between dimension \(n\) and smoothness of the Sobolev state space \(H^S(\Omega)\) providing a local exact controllability around any smooth solution of the cubic Schrödinger equation. The semigroup representation of the solution of associated linearized system plays a considerable role in the substantiation of results.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35B37
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 5555293
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: smoothing properties
zbMATH Keywords: exact boundary controllability
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: Neumann boundary conditions
MaRDI profile type: Publication
full work available at URL: j.jde.2008.11.004
OpenAlex ID: W1989537265
cites work: Controllability of a quantum particle in a moving potential well
cites work: Geometric control in the presence of a black box
cites work: Q4434430
cites work: Stabilization and control for the nonlinear Schrödinger equation on a compact surface
cites work: A weighted identity for partial differential operators of second order and its applications
cites work: Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit
cites work: Limitations on the control of Schrödinger equations
cites work: Q5749873
cites work: Controllability of the nonlinear Schrödinger equation in the vicinity of the ground state
cites work: Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet control
cites work: Q4669833
cites work: Control of the Schrödinger equation
cites work: Smoothing evolution equations and boundary control theory
cites work: Q3593001
cites work: Locally Distributed Control and Damping for the Conservative Systems
cites work: Exact Controllability for the Schrödinger Equation
cites work: Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights
cites work: How violent are fast controls for Schrödinger and plate vibrations?
cites work: Stabilization of a Boussinesq system of KdV-KdV type
cites work: Observability and control of Schrödinger equations
cites work: Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
cites work: Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain
cites work: CONTROL AND STABILIZATION OF THE NONLINEAR SCHRÖDINGER EQUATION ON RECTANGLES
cites work: Exact controllability and stabilizability of the Korteweg-de Vries equation
cites work: Compact sets in the space \(L^ p(0,T;B)\)
cites work: Exact Boundary Controllability of the Korteweg--de Vries Equation
DOI: 10.1016/J.JDE.2008.11.004
Recommended article: Exact boundary controllability of 1-D nonlinear Schrödinger equation
Recommended article: Exact Controllability for a Schrödinger Equation with Dynamic Boundary Conditions
Recommended article: Q3368520
Recommended article: Q4313597
Recommended article: Q4877087
Recommended article: Q5004846
Recommended article: Null boundary controllability of the Schrödinger equation with a potential
Recommended article: Exact Controllability for the Schrödinger Equation
Recommended article: Controllability of the nonlinear Schrödinger equation in the vicinity of the ground state
Recommended article: Q3358551
description: scientific article; zbMATH DE number 5555293