Controllability and Observability of Weakly Discontinuous Solutions for First Order Quasilinear Hyperbolic Systems

Based on the theory of the local exact boundary controllability and observability of the C1 solution for first order quasilinear hyperbolic systems,we obtain,by studying properties of weakly discontinuous solutions,the existence and uniqueness of the semi-global weakly discontinuous solution to the mixed initial-boundary value problem for first order quasilinear hyperbolic systems,in which the initial and boundary data have finite weak discontinuities,then we get the local exact boundary controllability and observability correspondingly.