{"paper":{"title":"Boundedness in a Keller-Segel system with external signal production","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2015-07-27T13:36:29Z","abstract_excerpt":"We study the Neumann initial-boundary problem for the chemotaxis system \\begin{align*} \\left\\{\\begin{array}{c@{\\,}l@{\\quad}l@{\\,}c} u_{t}&=\\Delta u-\\nabla\\!\\cdot(u\\nabla v),\\ &x\\in\\Omega,& t>0,\\\\ v_{t}&=\\Delta v-v+u+f(x,t),\\ &x\\in\\Omega,& t>0,\\\\ \\frac{\\partial u}{\\partial\\nu}&=\\frac{\\partial v}{\\partial\\nu}=0,\\ &x\\in\\partial\\Omega,& t>0,\\\\ u(x,0)&=u_{0}(x),\\ v(x,0)=v_{0}(x),\\ &x\\in\\Omega&\n  \\end{array}\\right. \\end{align*} in a smooth, bounded domain $\\Omega\\subset\\mathbb{R}^n$ with $n\\geq2$ and $f\\in\\text{L}^\\infty\\left([0,\\infty);\\text{L}^{\\frac{n}{2}+\\delta_0}(\\Omega)\\right)\\cap C^\\alpha(\\Om"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07400","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"}