A Degenerate Parabolic-Hyperbolic System Modeling the Spreading of Surfactants

We consider the initial-boundary value problem for a coupled parabolic-hyperbolic system for which the parabolic part degenerates. The problem arises in studying the spreading of surfactants on thin films, and the degeneracy occurs if either the surfactant concentration or the film height vanishes. Both cases will be considered. If the film height vanishes, the front does not advance. If, on the other hand, the surfactant concentration vanishes, then solutions with stationary or moving fronts are possible.