Analysis of the null-controllability of degenerate parabolic systems of Grushin type via the moments method - Archive ouverte HAL Access content directly
Journal Articles Journal of Evolution Equations Year : 2021

Analysis of the null-controllability of degenerate parabolic systems of Grushin type via the moments method

Abstract

In this article we compute the exact value of the minimal null control time for the Grushin equation controlled on a strip. This result is already known from a recent work by K. Beauchard, J. Dardé and S. Ervedoza but we propose a different approach based on the moments method. Our approach requires a careful spectral analysis of a truncated harmonic oscillator. We have also extended known results on biorthogonal families to real exponentials in the absence of a gap condition in order to obtain uniform estimates with respect to the asymptotic beahviour of the associated counting function. As a byproduct of our approach we also characterize the minimal null control time for systems of coupled Grushin equations with a distributed control on a strip or with a boundary control.
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Dates and versions

hal-02471592 , version 1 (08-02-2020)

Identifiers

  • HAL Id : hal-02471592 , version 1

Cite

Damien Allonsius, Franck Boyer, Morgan Morancey. Analysis of the null-controllability of degenerate parabolic systems of Grushin type via the moments method. Journal of Evolution Equations, 2021, 21, pp.4799-4843. ⟨hal-02471592⟩
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