Existence and stability of weak solutions for a degenerate parabolic   system modelling two-phase flows in porous media
  We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria. 
Joachim Escher (IFAM), Philippe Laurencot (IMT), Bogdan-Vasile Matioc   (IFAM)
math.AP