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Controllability of semilinear Schroedinger equation via low-dimensional source term

Author

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  • Andrey Sarychev

    (Dipartimento di Matematica per le Decisioni - Università degli Studi di Firenze)

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.

Suggested Citation

  • Andrey Sarychev, 2011. "Controllability of semilinear Schroedinger equation via low-dimensional source term," Working Papers - Mathematical Economics 2011-05, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    • Handle: RePEc:flo:wpaper:2011-05
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