{"paper":{"title":"How far does small chemotactic interaction perturb the Fisher-KPP dynamics?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit, Masaaki Mizukami","submitted_at":"2016-10-25T17:38:02Z","abstract_excerpt":"This paper deals with nonnegative solutions of the Neumann initial-boundary value problem for the fully parabolic chemotaxis-growth system $ (u_{\\varepsilon})_t$ $=\\Delta u_{\\varepsilon} - \\varepsilon \\nabla \\cdot ( u_\\varepsilon \\nabla v_\\varepsilon) + \\mu u_\\varepsilon(1 - u_\\varepsilon)$, $ (v_{\\varepsilon})_t=\\Delta v_\\varepsilon -v_\\varepsilon+u_\\varepsilon,$ with positive small parameter $\\varepsilon>0$ in a bounded convex domain $\\Omega\\subset\\mathbb{R}^n$ ($n\\geq 1$) with smooth boundary. The solutions converge to the solution $u$ to the Fisher-KPP equation as $\\varepsilon\\to 0$. It is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07981","kind":"arxiv","version":1},"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"}