Consider the Cauchy problem for a hyperbolic n× n system of conservation laws in one space dimension: uₜ + f(u)ₓ = 0, u(0,x)= u (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.
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Bressan et al. (2000) studied this question.