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

Damien Allonsius (1) , Franck Boyer (2, 3) , Morgan Morancey (1)

1 I2M - Institut de Mathématiques de Marseille
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 IUF - Institut universitaire de France

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.

Mots clés: Control theory; degenerate parabolic partial differential equations; minimal null control time; moments method; biorthogonal families; spectral analysis of harmonic oscillator

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

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⟩