{"paper":{"title":"A new result for global existence and boundedness of solutions to a parabolic--parabolic Keller--Segel system with logistic source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng, Yanyan Li","submitted_at":"2017-12-04T05:17:44Z","abstract_excerpt":"We consider the following fully parabolic Keller--Segel system with logistic source $$\n  \\left\\{\\begin{array}{ll}\n  u_t=\\Delta u-\\chi\\nabla\\cdot(u\\nabla v)+ au-\\mu u^2,\\quad x\\in \\Omega, t>0,\n  \\disp{v_t=\\Delta v- v +u},\\quad x\\in \\Omega, t>0,\n  \\end{array}\\right.\\eqno(KS) $$ over a bounded domain $\\Omega\\subset\\mathbb{R}^N(N\\geq1)$, with smooth boundary $\\partial\\Omega$, the parameters $a\\in \\mathbb{R}, \\mu>0, \\chi>0$. It is proved that if $\\mu>0$, then $(KS)$ admits a global weak solution, while if $\\mu>\\frac{(N-2)_{+}}{N}\\chi C^{\\frac{1}{\\frac{N}{2}+1}}_{\\frac{N}{2}+1}$, then $(KS)$ possess"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00906","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"}