Preprint A152/2002
A quasilinear parabolic system for three-phase capillary flow in porous media
A parabolic system is proposed to describe three-phase capillary flows in porous media. The assumptions imposed on the phase interaction mean that the capillarity matrix is triangular. The unique solvability of an associated non-degenerate parabolic system is proved for the Cauchy problem in a class of $x$-periodic solutions.