Nonnegative Weak Solutions for a Degenerate System Modeling the Spreading of Surfactant on Thin Films

Depending on the parameter range, we prove local and global in time existence of nonnegative weak solutions to a coupled system of two degenerate parabolic equations. This system models the spreading of an insoluble surfactant on a thin liquid film. This model includes gravity, surface tension, capillarity effects, and van der Waals forces. The surface diffusion coefficient is not assumed constant and depends on the surfactant concentration.