Volume 26, 2020
Special issue in honor of Enrique Zuazua's 60th birthday
|Number of page(s)||26|
|Published online||17 December 2020|
Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems
Shanghai Key Laboratory for Contemporary Applied Mathematics, Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University,
200433, P.R. China.
2 Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France.
3 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P.R. China.
* Corresponding author: email@example.com
Accepted: 22 September 2020
We show that under Kalman’s rank condition on the coupling matrices, the uniqueness of solution to a complex system of elliptic operators can be reduced to the observability of a scalar problem. Based on this result, we establish the asymptotic stability and the asymptotic synchronization for a large class of linear dissipative systems.
Mathematics Subject Classification: 93B05 / 93C20 / 35L53
Key words: uniqueness / elliptic systems / asymptotic synchronization / condition of compatibility / Kalman’s rank condition
© The authors. Published by EDP Sciences, SMAI 2020
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.