  The Buckley-Leverett equation for two phase flow in a porous medium is
modified by including a dependence of capillary pressure on the rate of change
of saturation. This model, due to Gray and Hassanizadeh, results in a nonlinear
pseudo-parabolic partial differential equation. Phase plane analysis, including
a separation function to measure the distance between invariant manifolds, is
used to determine when the equation supports traveling waves corresponding to
undercompressive shocks. The Riemann problem for the underlying conservation
law is solved and the structures of the various solutions are confirmed with
numerical simulations of the partial differential equation.
