Nonlinear Parabolic Equations with Spatial Discontinuities

Abstract.We consider a two phase flow involving no capillary barriers in a heterogeneous porous media, composed by an apposition of several homogeneous porous media. We prove the existence of a weak solution for such a flow using the convergence of a finite volume approximation. Then if the equations governing the flows in each homogeneous porous media degenerate in not too different ways, we prove the uniqueness of the weak solution, using a doubling variable method. We also prove that such a solution belongs to C([0, T], Lp(Ω)) for any p ∈ [1,+∞).