# Stabilization of Schrödinger equation in exterior domains

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

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

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topAloui, 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

top- L. Aloui and M. Khenissi, Stabilisation de l'équation des ondes dans un domaine extérieur. Rev. Math. Iberoamericana28 (2002) 1–16.
- N. Burq, Décroissance de l'énergie locale de l'équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel. Act. Math.1 (1998) 1–29.
- N. Burq, Semi-classical estimates for the resolvent in non trapping geometries. Int. Math. Res. Not.5 (2002) 221–241. Zbl1161.81368
- A. Jensen and T. Kato, Spectral properties of Schrödinger operators and time decay of the wave functions. Duke Math. J.46 (1979) 583–612. Zbl0448.35080
- M. Khenissi, Équation des ondes amorties dans un domaine extérieur. Bull. Soc. Math. France131 (2003) 211–228. Zbl1024.35061
- R.B. Melrose and J. Sjostrand, Singularities of boundary value problems I. Comm. Pure Appl. Math.31 (1978) 593–617. Zbl0368.35020
- C.S. Morawetz, Decay for solution of the exterior problem for the wave equation. Comm. Pure Appl. Math.28 (1975) 229–264. Zbl0304.35064
- J. Ralston, Solution of the wave equation with localized energy. Comm. Pure Appl. Math.22 (1969) 807–823. Zbl0209.40402
- J. Rauch, Local decay of scattering solutions of Schrödinger-type equation. Comm. Math. Phys.61 (1978) 149–168. Zbl0381.35023
- M. Reed and B. Simon, Methods of modern mathematical physics, Vol. I: Functional Analysis. New York, Academic Press (1972). Zbl0242.46001
- 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. Zbl0551.35069
- B. Vainberg, On the analytical properties of the resolvent for certain class of operator-pencils. Math. USSR-Sb.6 (1968) 241–273.
- 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. Zbl0294.35031
- B. Vainberg, On the short wave asymptotic behaviour of solutions of stationary problems and asymptotic behaviour as t$\u27f6+\infty $ of solutions of non-stationary problems. Russian Math. Surveys30 (1975) 1–58. Zbl0318.35006
- B. Vainberg, Asymptotic methods in equations of mathematical physics. Gordon and Breach, New York (1988).
- G. Vodev, On the uniform decay of the local energy. Serdica Math. J.25 (1999) 191–206. Zbl0937.35118
- H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains. Lect. Notes Math.442, Springer-Verlag (1975). Zbl0299.35002

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