Controllability of semilinear Schroedinger equation via low-dimensional source term

Andrey Sarychev ()
Additional contact information
Andrey Sarychev: Dipartimento di Matematica per le Decisioni - Università degli Studi di Firenze

No 2011-05, Working Papers - Mathematical Economics from Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa

Abstract: We study controllability of 2D defocusing cubic Schroedinger equation under periodic boundary conditions and control applied via source term (additively). The source term is a linear combination of few complex exponentials (modes) with time-variant coefficients - controls. We manage to prove that controlling just 4 modes one can achieve controllability of this equation in any finite-dimensional projection of its evolution space H^(1+\sigma), as well as approximate controllability in H^(1+\sigma) (\sigma>0). We also present negative result regarding exact controllability of cubic Schroedinger equation via a finite-dimensional source term.

Keywords: semilinear Schroedinger equation; approximate controllability; geometric control (search for similar items in EconPapers)
Pages: 25 pages
Date: 2011-05
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.disei.unifi.it/upload/sub/pubblicazioni ... 1/dimadwp2011-05.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:flo:wpaper:2011-05

Access Statistics for this paper

More papers in Working Papers - Mathematical Economics from Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa Via delle Pandette 9 50127 - Firenze - Italy. Contact information at EDIRC.
Bibliographic data for series maintained by Michele Gori ().