CRITICAL TIME FOR THE OBSERVABILITY OF KOLMOGOROV-TYPE EQUATIONS

Jérémi Dardé (1) , Julien Royer (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

This paper is devoted to the observability of a class of two-dimensional Kolmogorov-type equations presenting a quadratic degeneracy. We give lower and upper bounds for the critical time. These bounds coincide in symmetric settings, giving a sharp result in these cases. The proof is based on Carleman estimates and on the spectral properties of a family of non-selfadjoint Schrödinger operators, in particular the localization of the first eigenvalue and Agmon type estimates for the corresponding eigenfunctions.

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

Jérémi Dardé, Julien Royer. CRITICAL TIME FOR THE OBSERVABILITY OF KOLMOGOROV-TYPE EQUATIONS. Journal de l'École polytechnique — Mathématiques, 2021, ⟨10.5802/jep.160⟩. ⟨hal-02738864⟩