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Pré-Publication, Document De Travail Année : 2024

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

Yunlei Wang

Résumé

In this article, we prove null-controllability results for the heat equation associated to fractional 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.
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Dates et versions

hal-04245179 , version 1 (16-10-2023)
hal-04245179 , version 2 (12-02-2024)
hal-04245179 , version 3 (17-04-2024)

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Philippe Jaming, Yunlei Wang. Null-controllability of the Generalized Baouendi-Grushin heat like equations. 2024. ⟨hal-04245179v3⟩
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