Bounded traveling waves for a thin film with gravity and insoluble   surfactant
  Lubrication equations for a surfactant-driven flow of a thin layer of fluid are considered with a singular surfactant-dependent surface tension. It is shown that there exists a bounded traveling wave solution which connects a fully surfactant-coated film to an uncoated film. The regularity of the traveling wave depends on whether or not surface diffusion of the insoluble surfactant is included. 
Joachim Escher (IFAM), Matthieu Hillairet (CEREMADE, ICJ), Philippe   Laurencot (IMT), Christoph Walker (IFAM)
math.AP