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Lubrication equations for a surfactant-driven flow of a thin layer of fluidare considered with a singular surfactant-dependent surface tension. It isshown that there exists a bounded traveling wave solution which connects afully surfactant-coated film to an uncoated film. The regularity of thetraveling wave depends on whether or not surface diffusion of the insolublesurfactant is included.

Bounded traveling waves for a thin film with gravity and insoluble surfactant