On the Barenblatt Model for Non-Equilibrium Two Phase Flow in Porous Media

We prove global existence and uniqueness of solutions to a quasilinear Goursat problem, which was proposed by G. I. Barenblatt to describe non-equilibrium two phase fluid flow in permeable porous media. When the equilibrium relaxation time tends to zero, the solution is shown to converge to the entropy solution of the corresponding initial-boundary value problem for the classical Buckley-Leverett equation.