Finite difference schemes for the symmetric Keyfitz-Kranzer system

We are concerned with the convergence of numerical schemes for the initial value problem associated to the Keyfitz-Kranzer system of equations. This system is a toy model for several important models such as in elasticity theory, magnetohydrodynamics, and enhanced oil recovery. In this paper we prove the convergence of three difference schemes. Two of these schemes is shown to converge to the unique entropy solution. Finally, the convergence is illustrated by several examples.