{"paper":{"title":"A Simple Proof of Global Existence for the 1D Pressureless Gas Dynamics Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Fabio Cavalletti, Marc Sedjro, Michael Westdickenberg","submitted_at":"2013-11-13T12:49:46Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3108","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}