A UNIQUENESS THEOREM FOR WEAK SOLUTIONS OF SYMMETRIC QUASILINEAR HYPERBOLIC SYSTEMS

= 0 ot dx in the upper half-plane t ^ 0 if it satisfies the usual integral identity (defining "weak") together with the condition that, given a compact set D in t ^ 0, there exists a function Kit) e Lϊoc([0, oo)) such that Ui(xut)—ut(x2,t) Xί — X2 holds a.e. for xu x2eD and 0 < t < oo. It is shown that, if the matrix dJZf/du is symmetric and positive definite (a convexity condition), then weak solutions are uniquely determined by their initial conditions.