{"paper":{"title":"When do Keller-Segel systems with heterogeneous logistic sources admit generalized solutions?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianlu Yan, Mario Fuest","submitted_at":"2020-04-05T10:46:18Z","abstract_excerpt":"We construct global generalized solutions to the chemotaxis system\n  \\begin{align*}\n  \\begin{cases}\n  u_t = \\Delta u - \\nabla \\cdot (u \\nabla v) + \\lambda(x) u - \\mu(x) u^\\kappa,\\\\\n  v_t = \\Delta v - v + u\n  \\end{cases}\n  \\end{align*} in smooth, bounded domains $\\Omega \\subset \\mathbb R^n$, $n \\geq 2$, for certain choices of $\\lambda, \\mu$ and $\\kappa$.\n  Here, inter alia, the selections $\\mu(x) = |x|^\\alpha$ with $\\alpha < 2$ and $\\kappa = 2$as well as $\\mu \\equiv \\mu_1 > 0$ and $\\kappa > \\min\\{\\frac{2n-2}{n}, \\frac{2n+4}{n+4}\\}$ are admissible (in both cases for any sufficiently smooth $\\lam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.02153","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.02153/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}