{"paper":{"title":"Chemotaxis can prevent thresholds on population density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit","submitted_at":"2014-03-07T18:58:05Z","abstract_excerpt":"We define and (for $q>n$) prove uniqueness and an extensibility property of $W^{1,q}$-solutions to\n  $u_t =-\\nabla\\cdot(u\\nabla v)+\\kappa u-\\mu u^2$\n  $ 0 =\\Delta v-v+u$\n  $\\partial_\\nu v|_{\\partial\\Omega} = \\partial_\\nu u|_{\\partial\\Omega}=0,$ $ u(0,\\cdot)=u_0 $ in balls in $\\mathbb{R}^n$, which we then use to obtain a criterion guaranteeing some kind of structure formation in a corresponding chemotaxis system - thereby extending recent results of Winkler to the higher dimensional (radially symmetric) case.\n  Keywords: chemotaxis, logistic source, blow-up, hyperbolic-elliptic system"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1837","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"}