{"paper":{"title":"Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tobias Black","submitted_at":"2017-05-18T07:28:30Z","abstract_excerpt":"We investigate the parabolic-elliptic Keller-Segel model \\begin{align*}\\left\\{\\begin{array}{r@{\\,}l@{\\quad}l@{\\quad}l@{\\,}c} u_{t}&=\\Delta u-\\,\\chi\\nabla\\!\\cdot(\\frac{u}{v}\\nabla v),\\ &x\\in\\Omega,& t>0,\\\\ 0&=\\Delta v-\\,v+u,\\ &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),\\ &x\\in\\Omega,& \\end{array}\\right. \\end{align*} in a bounded domain $\\Omega\\subset\\mathbb{R}^n$ $(n\\geq2)$ with smooth boundary.\n  \\noindent We introduce a notion of generalized solvability which is consistent with the classical solution conce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06445","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"}