Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — the HUM Method

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.