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Given a system of two conservation laws which is admissible and satisfies the half-plane condition introduced by Keyfitz and Kranzer, the existence of a unique travelling-wave solution of the associated parabolic system, Ut 4F(U)X = s UXX9 which approximates a given shock, is proved. The shock profile trajectory is a convex curve in phase space, bounded by forward and backward shock curves.

Bounds for viscosity profiles for 2 X 2 systems of conservation laws