Comments on observability and stabilization of magnetic Schrödinger equations

Abstract : We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schrödinger equation to the magnetic Schrödinger equation. That is in presence of a magnetic potential. We establish observability inequalities and exponential stabilization by extending the usual multiplier method, under the same geometric condition to that needed for the Schrödinger equation. We also prove, with the help of elliptic Carleman inequalities, logarithmic stabilization results through a resol-vent estimate. Although the approach is classical, these results on logarithmic stabilization seem to be new even for the Schrödinger equation.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01634340
Contributeur : Mourad Choulli <>
Soumis le : mardi 14 novembre 2017 - 07:25:35
Dernière modification le : mercredi 14 novembre 2018 - 13:02:02
Document(s) archivé(s) le : jeudi 15 février 2018 - 12:52:48

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  • HAL Id : hal-01634340, version 1
  • ARXIV : 1711.05004

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Kaïs Ammari, Mourad Choulli, Luc Robbiano. Comments on observability and stabilization of magnetic Schrödinger equations. 2017. 〈hal-01634340〉

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