Convergence of approximate solutions of the Cauchy problem for a 2 × 2 nonstrictly hyperbolic system of conservation laws

A convergence theorem for the vanishing viscosity method and for the Lax-Friedrichs schemes, applied to a nonstrictly hyperbolic and nongenuinely nonlinear system is established. Using the theory of compensated compactness we prove convergence of a subsequence in the strong topology.