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- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2019
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-019-09640-8
- Publisher site
- See Article on Publisher Site
Abstract
The main purpose of this paper is to show the global stabilization and exact controllability properties of a fourth order nonlinear Schrödinger system on a periodic domain T\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {T}$$\end{document} with internal control supported on an arbitrary sub-domain of T\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {T}$$\end{document}. More precisely, by certain properties of propagation of compactness and regularity in Bourgain spaces, for the solutions of the associated linear system, we show that the system is globally exponentially stabilizable. This property together with the local exact controllability shows that fourth order nonlinear Schrödinger is globally exactly controllable.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Dec 7, 2019
Keywords: Bourgain spaces; Exact controllability; Fourth order nonlinear Schrödinger; Propagation of compactness; Propagation of regularity; Stabilization; Primary 35Q55; Secondary 93B05; 93D15; 35A21