The interface dynamics of a surfactant drop on a thin viscous film

Abstract

We study a system of two coupled parabolic equations that models the spreading of a drop of an insoluble surfactant on a thin liquid film. Unlike the previously known results, the surface diffusion coefficient is not assumed constant and depends on the surfactant concentration. We obtain sufficient conditions for finite speed of support propagation and for waiting-time phenomenon by application of an extension of Stampacchia's lemma for a system of functional equations.