Critical time for the observability of Kolmogorov-type equations

Abstract

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.

References in corpus (3)

• Controllability of a 2x2 parabolic system by one force with a space-dependent coupling term of order one
• Time optimal observability for Grushin Schrödinger equation
• On the semi-classical analysis of Schrödinger operators with purely imaginary electric potentials in a bounded domain

Cited by in corpus (1)

• Exact observability properties of subelliptic wave and Schr{ö}dinger equations