Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.11215 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917644367560704 |
|---|---|
| author | Jaming, Philippe Wang, Yunlei |
| author_facet | Jaming, Philippe Wang, Yunlei |
| contents | In this article, we prove null-controllability results for the heat equation associated tofractional Baouendi-Grushin operators $$\partial_t u+\bigl(-Δ_x-V(x)Δ_y\bigr)^s u= \mathbb{1}_Ωh$$ where $V$ is a potential that satisfies some power growth conditions and the set $Ω$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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11215 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Null-controllability of the Generalized Baouendi-Grushin heat like equations Jaming, Philippe Wang, Yunlei Optimization and Control In this article, we prove null-controllability results for the heat equation associated tofractional Baouendi-Grushin operators $$\partial_t u+\bigl(-Δ_x-V(x)Δ_y\bigr)^s u= \mathbb{1}_Ωh$$ where $V$ is a potential that satisfies some power growth conditions and the set $Ω$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. |
| title | Null-controllability of the Generalized Baouendi-Grushin heat like equations |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2310.11215 |