Volume 26, 2020
Special issue in the 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: firstname.lastname@example.org
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
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