Stabilization of Schrödinger equation in exterior domains

Lassaad Aloui; Moez Khenissi

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 3, page 570-579
  • ISSN: 1292-8119

Abstract

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We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties.

How to cite

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Aloui, Lassaad, and Khenissi, Moez. "Stabilization of Schrödinger equation in exterior domains." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 570-579. <http://eudml.org/doc/250004>.

@article{Aloui2007,
abstract = { We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties. },
author = {Aloui, Lassaad, Khenissi, Moez},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Cut-off resolvent; local energy decay; stabilization; cut-off resolvent},
language = {eng},
month = {6},
number = {3},
pages = {570-579},
publisher = {EDP Sciences},
title = {Stabilization of Schrödinger equation in exterior domains},
url = {http://eudml.org/doc/250004},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Aloui, Lassaad
AU - Khenissi, Moez
TI - Stabilization of Schrödinger equation in exterior domains
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/6//
PB - EDP Sciences
VL - 13
IS - 3
SP - 570
EP - 579
AB - We prove uniform local energy estimates of solutions to the damped Schrödinger equation in exterior domains under the hypothesis of the Exterior Geometric Control. These estimates are derived from the resolvent properties.
LA - eng
KW - Cut-off resolvent; local energy decay; stabilization; cut-off resolvent
UR - http://eudml.org/doc/250004
ER -

References

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  10. M. Reed and B. Simon, Methods of modern mathematical physics, Vol. I: Functional Analysis. New York, Academic Press (1972).  
  11. Y. Tsutsumi, Local energy decay of solutions to the free Schrödinger equation in exterior domains. J. Fac. Sci. Univ. Tokyo, Sect. IA, Math.31 (1984) 97–108.  
  12. B. Vainberg, On the analytical properties of the resolvent for certain class of operator-pencils. Math. USSR-Sb.6 (1968) 241–273.  
  13. B. Vainberg, On the exterior elliptic problems polynomially depending on a spectral parameters, and asymptotic behaviour for large time of solutions of non stationary problems. Math. USSR-Sb.21 (1973) 221–239.  
  14. B. Vainberg, On the short wave asymptotic behaviour of solutions of stationary problems and asymptotic behaviour as t ⟶ + ∞ of solutions of non-stationary problems. Russian Math. Surveys30 (1975) 1–58.  
  15. B. Vainberg, Asymptotic methods in equations of mathematical physics. Gordon and Breach, New York (1988).  
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  17. H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains. Lect. Notes Math.442, Springer-Verlag (1975).  

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