Spectral Analysis of Fronts in a Marangoni-Driven Thin Liquid Film Flow Down a Slope

We consider a model that describes a flow of a thin liquid film modified by insoluble surfactant which is moving down a slope. For this model, parameter regimes were previously identified when the system supports traveling fronts. We use a combination of analytic and numerical techniques such as Evans function calculations to investigate the spectral stability of traveling fronts for a selection of values from each of these parameter regimes....