Issue |
ESAIM: COCV
Volume 26, 2020
Special issue in honor of Enrique Zuazua's 60th birthday
|
|
---|---|---|
Article Number | 117 | |
Number of page(s) | 26 | |
DOI | https://doi.org/10.1051/cocv/2020062 | |
Published online | 17 December 2020 |
Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems
1
Shanghai Key Laboratory for Contemporary Applied Mathematics, Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University,
Shanghai
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: rao@math.unistra.fr
Received:
3
July
2020
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.
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