{"paper":{"title":"The fast signal diffusion limit in a Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami","submitted_at":"2017-11-12T17:52:13Z","abstract_excerpt":"This paper deals with convergence of a solution for the parabolic-parabolic Keller-Segel system \\[ (u_\\lambda)_t = \\Delta u_\\lambda - \\chi \\nabla \\cdot (u_\\lambda \\nabla v_\\lambda), \\quad \\lambda (v_\\lambda)_t = \\Delta v_\\lambda - v_\\lambda + u_\\lambda \\quad \\mbox{in} \\ \\Omega\\times (0,\\infty) \\] to that for the parabolic-elliptic Keller-Segel system \\[ u_t = \\Delta u - \\chi \\nabla \\cdot (u \\nabla v), \\quad 0= \\Delta v -v +u \\quad \\mbox{in} \\ \\Omega\\times (0,\\infty) \\] as $\\lambda \\searrow 0$, where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ ($n\\ge 2$) with smooth boundary, $\\chi, \\lambda>"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04328","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"}