A uniqueness condition for hyperbolic systems of conservation laws

Consider the Cauchy problem for a hyperbolic n x n system of conservation laws in one space dimension: u(t) + f(u)(x) = 0, u(0, x) = (u) over bar(x). (CP) Relying on the existence of a continuous semigroup of solutions, we prove that the entropy admissible solution of (CP) is unique within the class of functions u = u(t, x) which have bounded variation along a suitable family of space-like curves.