Abstract
Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown in recent work by Natile and Savare. Their proof uses a discrete particle approximation and stability properties for first-order differential inclusions. Here we give a more direct proof that relies on a result by Haraux on the differentiability of metric projections. We apply the same method also to the one-dimensional Euler--Poisson system, obtaining a new proof for the global existence of weak solutions.
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