Control of the Grushin equation: non-rectangular control region and minimal time

Abstract

This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangular control region. We establish the positive result thanks to the fictitious control method and the negative one by interpreting the associated observability inequality as an $L^2$ estimate on complex polynomials.

References in corpus (4)

• Non null controllability of the Grushin equation in 2D
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• Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms
• Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems

Cited by in corpus (7)

• Time optimal observability for Grushin Schrödinger equation
• Subelliptic wave equations are never observable
• Sharp resolvent estimate for the Baouendi-Grushin operator and applications
• Unique continuation estimates for Baouendi--Grushin equations on cylinders
• Critical time for the observability of Kolmogorov-type equations
• Exact observability properties of subelliptic wave and Schr{ö}dinger equations
• Null-controllability of the Generalized Baouendi-Grushin heat like equations