Null-controllability of the Generalized Baouendi-Grushin heat like equations

Abstract

In this article, we prove null-controllability results for the heat equation associated tofractional Baouendi-Grushin operators $${\partial }_{t}u+(-{\Delta }_x-V(x){\Delta }_y{)}^{s}u=1_{\Omega }h$$ where $V$ is a potential that satisfies some power growth conditions and the set $\Omega$is thick in some sense. This extends previously known results for potentials $V(x)=|x{|}^{2k}$.To do so, we study Zhu-Zhuge's spectral inequality for Schr{ö}dinger operators with power growth potentials, and give a precised quantitative form of it.

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