The Lifshitz-Slyozov system with inflow boundary conditions

The Lifshitz-Slyozov system describes a mixture of monomers and aggregates, where monomers can attach to or detach from already existing clusters. The aggregate distribution solves a transport equation with respect to a size variable, whose transport rates are coupled to the dynamic of monomers in a nonlocal fashion. Recent applications require a nonlinear boundary condition at zero size. We analyze the well-posedness of the resulting model, showing the existence and uniqueness of local-in-time solutions, together with continuation criteria. We also give partial results on global existence and the related long time behavior.