| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/cocv/2019001 | |
| Published online | 13 January 2020 | |
Control of the Grushin equation: non-rectangular control region and minimal time*,**
1
Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions,
75005,
Paris, France.
2
Université Côte d’Azur, CNRS,
LJAD, France.
*** Corresponding author: mduprez@math.cnrs.fr
Received:
3
July
2018
Accepted:
11
January
2019
This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangular control regions. We establish the positive result thanks to the fictitious control method and the negative one by interpreting the associated observability inequality as an L2 estimate on complex polynomials.
Mathematics Subject Classification: 93B05 / 93C20 / 35K65
Key words: Controllability / minimal time / degenerated parabolic equations
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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