Comments on observability and stabilization of magnetic Schr{\"o}dinger equations

Kaïs Ammari; Mourad Choulli; Luc Robbiano

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arXiv · 1711.05004

Comments on observability and stabilization of magnetic Schr{\"o}dinger equations

Kaïs Ammari·Mourad Choulli·Luc Robbiano

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Abstract

We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schr{\"o}dinger equation to the magnetic Schr{\"o}dinger 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 Schr{\"o}dinger equation. We also prove, with the help of elliptic Carleman inequalities, logarithmic stabilization results through a resolvent estimate. Although the approach is classical, these results on logarithmic stabilization seem to be new even for the Schr{\"o}dinger equation.

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Kaïs Ammari, Mourad Choulli, Luc Robbiano. 2017-11-14. Comments on observability and stabilization of magnetic Schr{\"o}dinger equations. https://arxiv.org/abs/1711.05004

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