This is a survey on some properties of non-convex hyperbolic conservation law. In this paper, an overview of basic knowledge and a domestic and international studies of hyperbolic conservation law are provided; some properties of non-convex hyperbolic conservation law are illustrated mainly. Generally speaking, there are four parts in this paper. In the first part , some preliminaries are given; In the second part, some important results on the fields are dealt with; In the third, the structures and regularities of solvers of Riemann problem of non-convex hyperbolic conservation law are studied; In the last part, a number of issues to be answered are given. |