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arXiv · 1910.03691

Time optimal observability for Grushin Schrödinger equation

Nicolas Burq·Chenmin Sun
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Abstract

We consider two dimensional Grushin Schrödinger equation posed on a finite cylinder $Ω=(-1,1)_x\times \T_y$ with Dirichlet boundary condition. We obtain the sharp observability by any horizontal strip, with the optimal time $T_*>0$ depending on the size of the strip. Consequently, we prove the exact controllability for Grushin Schrödinger equation. By exploiting the concentration of eigenfunctions of harmonic oscillator at $x=0$, we also show that the observability fails for any $T\leq T_*$.

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Nicolas Burq, Chenmin Sun. 2021-03-19. Time optimal observability for Grushin Schrödinger equation. https://doi.org/10.2140/apde.2022.15.1487

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