Null-controllability of the Generalized Baouendi-Grushin heat like equations
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en
Document de travail - Pré-publication
Résumé en anglais
In this article, we prove null-controllability results for the heat equation associated tofractional Baouendi-Grushin operators $$\partial_t u+\bigl(-\Delta_x-V(x)\Delta_y\bigr)^s u=\un_\Omega h$$where $V$ is a potential ...Lire la suite >
In this article, we prove null-controllability results for the heat equation associated tofractional Baouendi-Grushin operators $$\partial_t u+\bigl(-\Delta_x-V(x)\Delta_y\bigr)^s u=\un_\Omega h$$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 Schrödinger operators with power growth potentials, and give a precised quantitative form of it.< Réduire
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