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. © 2015 Society for Industrial and Applied Mathematics.

A simple proof of global existence for the 1D pressureless gas dynamics equations

Cavalletti, Fabio;
2015

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 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. © 2015 Society for Industrial and Applied Mathematics.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
47
1
66
79
http://dx.medra.org/10.1137/130945296
https://arxiv.org/abs/1311.3108
Cavalletti, Fabio; Sedjro, M.; Westdickenberg, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/44726
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