Abstract
We study the shock dynamics for a recently proposed system of conservation laws (Murisic et al. [J. Fluid Mech., 17 (2013), pp. 203--231]) describing gravity-driven thin-film flow of a suspension of negatively buoyant particles down an incline. When the particle concentration is above a critical value, singular shock solutions can occur. We analyze the Hugoniot topology associated with the Riemann problem for this system, describing in detail how the transition from a double shock to a singular shock happens. We also derive the singular shock speed based on a key observation that the particles pile up at the maximum packing fraction near the contact line.
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