Viscous singular shock profiles for a system of conservation laws modeling two-phase flow

This paper is concerned with singular shocks for a system of conservation laws via the Dafermos regularization ut+f(u)x=ϵtuxxut+f(u)x=ϵtuxx. For a system modeling incompressible two-phase fluid flow, the existence of viscous profiles is proved using Geometric Singular Perturbation Theory. The weak convergence and the growth rate of the viscous solution are also derived; the weak limit is the sum of a piecewise constant function and a δ  -measure supported on a shock line, and the maximum value of the viscous solution is of order exp⁡(1/ϵ)exp⁡(1/ϵ).