{"paper":{"title":"Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler, Youshan Tao","submitted_at":"2016-08-26T22:53:11Z","abstract_excerpt":"We study the Neumann initial-boundary problem for the chemotaxis system $$  \\left\\{\\begin{array}{ll} u_t= \\Delta u - \\nabla \\cdot (u\\nabla v), & x\\in \\Omega, \\, t>0, 0=\\Delta v - \\mu(t)+w, & x\\in \\Omega, \\, t>0, \\tau w_t + \\delta w = u, & x\\in \\Omega, \\, t>0, \\end{array} \\right. \\qquad \\qquad (\\star) $$ in the unit disk $\\Omega:=B_1(0)\\subset \\R^2$, where $\\delta\\ge 0$ and $\\tau>0$ are given parameters and $\\mu(t):=\\mint_\\Omega w(x,t)dx$, $t>0$. It is shown that this problem exhibits a novel type of critical mass phenomenon with regard to the formation of singularities, which drastically diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07622","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"}