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Time optimal
observability for Grushin Schrödinger equation
Nicolas Burq and Chenmin Sun |
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Vol. 15 (2022), No. 6, 1487–1530
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Abstract |
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We consider the two-dimensional Grushin Schrödinger equation posed on a finite cylinder with Dirichlet boundary condition. We obtain sharp observability by any horizontal strip, with the optimal time depending on the size of the strip. Consequently, we prove the exact controllability for the Grushin Schrödinger equation. By exploiting the concentration of eigenfunctions of a harmonic oscillator at , we also show that the observability fails for any . |
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Keywords
controllability, observability, subelliptic, Schrödinger
equation, semiclassical analysis
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Mathematical Subject Classification 2010
Primary: 35Q41, 35Q93, 93B07
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Milestones
Received: 9 October 2019
Revised: 2 February 2021
Accepted: 19 March 2021
Published: 10 November 2022
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Authors |
| Nicolas Burq | |
| Université Paris-Sud, Université
Paris-Saclay and Institut Universitaire de France, Laboratoire
de Mathématiques d’Orsay, UMR 8628 du CNRS Orsay France |
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| Chenmin Sun | |
| Université de Cergy-Pontoise,
Laboratoire de Mathématiques AGM, UMR 8088 du CNRS Cergy-Pontoise France |
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