Non-local parabolic systems: applications in the three-phase capillary fluid filtration
V. V. Shelukhin, Cezar I. Kondo · European Journal of Applied Mathematics · 2005
Non-local degenerate parabolic systems arise in three-phase capillary flows in porous media under a pressure control at the inflow- and outflow-boundaries. A mathematical study of such systems is performed for a class of capillarity pressure functions corresponding to triangular capillarity-diffusion tensors. To this end a theory of non-degenerate parabolic approximations is developed: the unique global solvability of initial boundary-value problems is proved.