Convergence of the Fractional Step Method for a 2 3 2 Nonstrictly Hyperbolic System of Conservation Laws

We study the existence of solutions to the Cauchy problem for a non-homogeneous nonstrictly hyperbolic system of 2 3 2 conservation laws, satisfying the Lax entropy inequality. We obtain the convergence and the consistency of the approximating sequences generated by either the fractional Lax–Friedrichs or the fractional Godunov scheme. For this purpose we use the methods of the theory of compensated compactness. Ó 1996 Academic Press, Inc.