Weak solutions to a thin film model with capillary effects and insoluble   surfactant
  The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and coupled to a second order parabolic equation for the surfactant concentration. It is shown that nonnegative weak solutions exist under natural assumptions on the surface tension coefficient. 
Joachim Escher (IFAM), Matthieu Hillairet (CEREMADE), Philippe   Laurencot (IMT), Christoph Walker (IFAM)
math.AP