Comments on observability and stabilization of magnetic Schr{\"o}dinger equations
Analysis of PDEs
2019-09-04 v2
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.
Keywords
Cite
@article{arxiv.1711.05004,
title = {Comments on observability and stabilization of magnetic Schr{\"o}dinger equations},
author = {Kaïs Ammari and Mourad Choulli and Luc Robbiano},
journal= {arXiv preprint arXiv:1711.05004},
year = {2019}
}