Convergence of the fractional step method for a 2 x 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 x 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. (C) 1996 Academic Press, Inc.