Controllability And Observability Of Weakly Discontinuous Solutions For First Order Quasilinear Hyperbolic Systems

This thesis is divided into four parts. In the first part, we give the definition of the exact boundary controllability and observability, the history of the related study and some preliminaries. In the second part, we give the definition of weakly discontinuous solution and study its properties. In the third part, by means of the results given in the second part, we prove the existence and uniqueness of the semi-global weakly discon-tinuous solution to the mixed initial-boundary value problem for first order qusilinear hyperbolic systems,in which the initial and boundary date have finite weak discontini-ties.In the fourth part,we give the local exact boundary controllability and observability of weakly discontinuous solutions for general first order quasilinear hyperbolic systems...