Critical time for the observability of Kolmogorov-type equations
Analysis of PDEs
2022-07-06 v1 Optimization and Control
Spectral Theory
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 Schr\"odinger operators, in particular the localization of the first eigenvalue and Agmon type estimates for the corresponding eigenfunctions.
Keywords
Cite
@article{arxiv.2006.01753,
title = {Critical time for the observability of Kolmogorov-type equations},
author = {Jérémi Dardé and Julien Royer},
journal= {arXiv preprint arXiv:2006.01753},
year = {2022}
}