A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics Equations
| Autor: | Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Pressureles gas dynamics
Applied Mathematics Mathematical analysis Stability (probability) Computational Mathematics Monotone polygon Mathematics - Analysis of PDEs Differential inclusion Cone (topology) Simple (abstract algebra) Settore MAT/05 - Analisi Matematica Mathematics - Classical Analysis and ODEs Metric (mathematics) Optimal transport Classical Analysis and ODEs (math.CA) FOS: Mathematics Direct proof Differentiable function 35L65 49J40 82C40 Analysis Mathematics Analysis of PDEs (math.AP) |
| Popis: | 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 Savar\'{e}. 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. Comment: 15 pages, added Euler-Poisson system |
| Databáze: | OpenAIRE |
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