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.
Titolo: | A simple proof of global existence for the 1D pressureless gas dynamics equations |
Autori: | Cavalletti, F.; Sedjro, M.; Westdickenberg, M. |
Rivista: | |
Data di pubblicazione: | 2015 |
Volume: | 47 |
Fascicolo: | 1 |
Pagina iniziale: | 66 |
Pagina finale: | 79 |
Digital Object Identifier (DOI): | 10.1137/130945296 |
URL: | http://dx.medra.org/10.1137/130945296 https://arxiv.org/abs/1311.3108 |
Appare nelle tipologie: | 1.1 Journal article |
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