On the Barenblatt model for non-equilibrium two phase flow in porous media

We prove global existence and uniqueness of solutions to a quasilinear Gour sat problem, which was proposed by G. I. Barenblatt to describe non-equilib rium two phase fluid flow in permeable porous media. When the equilibrium r elaxation time tends to zero, the solution is shown to converge to the entr opy solution of the corresponding initial-boundary value problem for the cl assical Buckley-Leverett equation.