Time optimal observability for Grushin Schrödinger equation

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 $T_{\ast }>0$ 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 $T\le T_{\ast }$.

arXiv comment47 pages, 3 figures

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Cited by in corpus (6)

• Observability of Baouendi-Grushin-Type Equations Through Resolvent Estimates
• Subelliptic wave equations are never observable
• Logarithmic decay for damped hypoelliptic wave and Schr{ö}dinger equations
• Sharp resolvent estimate for the Baouendi-Grushin operator and applications
• Critical time for the observability of Kolmogorov-type equations
• Exact observability properties of subelliptic wave and Schr{ö}dinger equations