Viscous singular shock structure for a nonhyperbolic two-fluid model

We consider a system of two nonhyperbolic conservation laws modelling incompressible two-phase flow in one space dimension. The purpose of this paper is to justify the use of singular shocks in the solution of Riemann problems. We prove that both strictly and weakly overcompressive singular shocks are limits of viscous structures. Using Riemann solutions we solve Cauchy problems with piecewise constant data for the nonhyperbolic two-fluid model.