{"paper":{"title":"Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emanuela Radici, Simone Fagioli","submitted_at":"2018-01-30T17:50:10Z","abstract_excerpt":"We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegative initial data in $L^{\\infty} \\cap BV$ away from vacuum and supported in a closed interval with zero-velocity boundary conditions. The main novelties of this work concern the presence of a nonlinear mobility term and the non strict monotonicity of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10114","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"}