Data di Pubblicazione:
2015
Citazione:
A simple proof of global existence for the 1D pressureless gas dynamics equations / F. Cavalletti, M. Sedjro, M. Westdickenberg. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 47:1(2015), pp. 66-79. [10.1137/130945296]
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Optimal transport; Pressureles gas dynamics;
Elenco autori:
F. Cavalletti, M. Sedjro, M. Westdickenberg
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