Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 74 | |
Number of page(s) | 33 | |
DOI | https://doi.org/10.1051/cocv/2024042 | |
Published online | 07 October 2024 |
Asymptotic behavior of null controllability cost for parabolic equations with vanishing diffusivity under Robin and Neumann boundary conditions
1
Lab-SIV, Faculty of Sciences-Agadir, Ibnou Zohr University, B.P. 8106, Agadir, Morocco
2
Department of Mathematics, University of the Basque Country UPV/EHU, Barrio Sarriena s/n, 48940 Leioa, Spain
3
Lab-SIV, Polydisciplinary Faculty-Ouarzazate, Ibnou Zohr University, BP 638, Ouarzazate 45000, Morocco
4
Cadi Ayyad University, Faculty of Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC) B.P. 2390, Marrakesh, Morocco
5
Mohammed VI Polytechnic University, Vanguard-Center, Green City, Morocco
* Corresponding author: jonasier.barcena@ehu.eus
Received:
17
June
2023
Accepted:
8
May
2024
In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the control cost decays exponentially when the viscosity vanishes and the control time is sufficiently large. On the other hand, if the range of the control region by the transport flow does not cover that of Ω, we prove that the control cost explodes exponentially for the Neumann boundary conditions case with vanishing viscosity and all control time.
Mathematics Subject Classification: 35B25 / 35K05 / 93B05 / 93C20
Key words: Carleman estimates / uniform controllability / transport equation / singular limits / cost control / spectral decomposition
© The authors. Published by EDP Sciences, SMAI 2024
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.