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| Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — the HUM Method* |
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Citation： |
Xing LU,Tatsien LI.Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — the HUM Method*[J].Chinese Annals of Mathematics B,2022,43(1):1~16 |
| Page view： 637
Net amount： 541 |
Authors： |
Xing LU; Tatsien LI |
Foundation： |
National Natural Science Foundation of China (Nos. 11831011,11901082), the Natural Science Foundation of Jiangsu Province (No. BK20190323) and the Fundamental Research Funds for the Central Universities of China. |
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| Abstract： |
The exact boundary controllability and the exact boundary observability for the 1-D first order linear hyperbolic system were studied by the constructive method in the framework of weak solutions in the work [Lu, X. and Li, T. T., Exact boundary controllability of weak solutions for a kind of first order hyperbolic system — the constructive method, Chin. Ann. Math. Ser. B, 42(5), 2021, 643–676]. In this paper, in order to study these problems from the viewpoint of duality, the authors establish a complete theory on the HUM method and give its applications to first order hyperbolic systems. Thus, a deeper relationship between the controllability and the observability can be revealed.Moreover, at the end of the paper, a comparison will be made between these two methods. |
Keywords： |
First order linear hyperbolic system, Exact boundary controllability,The HUM method |
Classification： |
93B05, 93C20, 35L50 |
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