A Quasi-linear Parabolic System for Three-Phase Capillary Flow in Porous Media
Hermano Frid, V. V. Shelukhin · SIAM Journal on Mathematical Analysis · 2003
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 nondegenerate parabolic system is proved for the Cauchy problem in a class of x-periodic solutions.