Communications of the
Korean Mathematical Society CKMS

We prove that solutions $u^{\epsilon}$ for the mixed hyperbolic-elliptic system of conservation laws with the viscosity term are total variation bounded uniformly in $\epsilon$ and that the solution $u^{\epsilon}$ converges to the solution for the mixed hyperbolic-elliptic Riemann problem as $\epsilon\to 0$.

Keywords: Riemann problem, existence of solutions, fixed point theorem

MSC numbers: 35L45, 35L65