Simple waves and shocks in a thin film of a perfectly soluble anti-surfactant solution

We consider the dynamics of a thin film of a perfectly soluble anti-surfactant solution in the limit of large capillary and Peclet numbers in which the governing system of nonlinear equations is purely hyperbolic. We construct exact solutions to a family of Riemann problems for this system, and discuss the properties of these solutions, including the formation of both simple-wave and uniform regions within the flow, and the propagation of shocks in both the thickness of the film and the gradient of the concentration of solute