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| Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems II: Case of Multiple Feedback Dampings* |
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Citation： |
Tatsien LI,Bopeng RAO.Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems II: Case of Multiple Feedback Dampings*[J].Chinese Annals of Mathematics B,2022,43(5):659~684 |
| Page view： 402
Net amount： 340 |
Authors： |
Tatsien LI; Bopeng RAO |
Foundation： |
National Natural Science Foundation of China (No.11831011). |
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| Abstract： |
In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings. They ?rst show that under the observability of a scalar equation, Kalman’s rank condition is su?cient for the uniqueness of solution to a complex system of elliptic equations with mixedobservations. The authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various natures. Some classic models are presented to illustrate the ?eld of applications of the abstract theory. |
Keywords： |
Kalman rank condition, Uniqueness, Asymptotic synchronization, Kelvin-Voigt damping |
Classification： |
93B05, 93C20, 35L53 |
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