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 ...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 con-trollability 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 the-ory 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.展开更多
基金This work was supported by the National Natural Science Foundation of China(Nos.11831011,11901082)the Natural Science Foundation of Jiangsu Province(No.BK20190323)the Fundamental Research Funds for the Central Universities of China.
文摘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 con-trollability 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 the-ory 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.
