| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 15 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/cocv/2023002 | |
| Published online | 27 February 2023 | |
Controllability and observability for some forward stochastic complex degenerate/singular Ginzburg–Landau equations*
1
Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
2
School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, China
** Corresponding author: zhaoqm@stu.scu.edu.cn
Received:
15
May
2022
Accepted:
28
December
2022
This paper is addressed to establishing controllability and observability for some forward linear stochastic complex degenerate/singular Ginzburg-Landau equations. It is sufficient to establish appropriate observability inequalities for the corresponding backward and forward equations. The key is to prove the Carleman estimates of the forward and backward linear stochastic complex degenerate/singular Ginzburg-Landau operators. Compared with the existing deterministic results, it is necessary to overcome the difficulties caused by some complex coefficients and random terms. The results obtained cover those of deterministic cases and generalize those of stochastic degenerate parabolic equations. Moreover, the limit behavior of the coefficients in the equation is discussed.
Mathematics Subject Classification: 93B05 / 93B07
Key words: Stochastic degenerate/singular Ginzburg-Landau equation / controllability / observability / Carleman estimate
This work is partially supported by the NSF of China under grant 11971333, 11931011, the Postdoctoral Science Foundation of China under grants 2021TQ0353, and the Science Development Project of Sichuan University under grant 2020SCUNL201. The authors gratefully acknowledges Professor Xiaoyu Fu and Professor Xu Liu for their guidance and suggestions.
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://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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