{"paper":{"title":"Classical solutions to a logistic chemotaxis model with singular sensitivity and signal absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elisa Lankeit, Johannes Lankeit","submitted_at":"2018-03-11T18:38:07Z","abstract_excerpt":"Assuming that $0<\\chi<\\sqrt{\\frac{2}n}$, $\\kappa\\ge 0$ and $\\mu>\\frac{n-2}{n}$, we prove global existence of classical solutions to a chemotaxis system slightly generalizing \\[ \\begin{split} u_t &= \\Delta u - \\chi \\nabla\\cdot ( \\frac{u}{v} \\nabla v ) + \\kappa u -\\mu u^2\\\\ v_t &= \\Delta v - u v \\end{split} \\] in a bounded domain $\\Omega \\subset \\mathbb{R}^n$, with homogeneous Neumann boundary conditions and for widely arbitrary positive initial data. In the spatially one-dimensional setting, we prove global existence and, moreover, boundedness of the solution for any $\\chi>0$, $\\mu>0$, $\\kappa\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04006","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"}