{"paper":{"title":"Large mass boundary condensation patterns in the stationary Keller-Segel system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Giusi Vaira, Manuel del Pino","submitted_at":"2014-03-11T09:21:32Z","abstract_excerpt":"We consider the boundary value problem $-\\Delta u + u =\\lambda e^u$ in $\\Omega$ with Neumann boundary condition, where $\\Omega$ is a bounded smooth domain in $\\mathbb R^2$, $\\lambda>0.$ This problem is equivalent to the stationary Keller-Segel system from chemotaxis. We establish the existence of a solution $u_\\lambda$ which exhibits a sharp boundary layer along the entire boundary $\\partial\\Omega$ as $\\lambda\\to 0$. These solutions have large mass in the sense that $ \\int_\\Omega \\lambda e^{u_\\lambda} \\sim |\\log\\lambda|.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2511","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"}