2013/11/13 by Fabio Cavalletti, Cavalletti, Fabio, Marc Sedjro +3
Mathematics · #35L65 #49J40 #82C40 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AP #math.CA #msc:35L65 #msc:49J40 #msc:82C40
paper · pdf · doi:10.48550/arxiv.1311.3108
15 pages, added Euler-Poisson system
arxiv created 2014/11/19 · arxiv updated 2014/11/20
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 Savaré. 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.