{"paper":{"title":"A new result for boundedness in the quasilinear parabolic-parabolic Keller-Segel model (with logistic source)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2018-08-10T13:51:01Z","abstract_excerpt":"The current paper considers the boundedness of solutions to the following quasilinear Keller-Segel model (with logistic source) $$\\left\\{\\begin{array}{ll} u_t = \\nabla\\cdot(D(u)\\nabla u)-\\chi\\nabla\\cdot(u\\nabla v)+\\mu (u-u^2),\\quad x\\in \\Omega, t>0,\\\\ v_t-\\Delta v = u-v,\\quad x\\in \\Omega, t>0,\\\\ (D(u)\\nabla u-\\chi u\\cdot \\nabla v)\\cdot \\nu = \\frac{\\partial v}{\\partial\\nu}=0,\\quad x\\in \\partial\\Omega, t>0,\\\\  u(x,0) = u_0(x),\\quad v(x,0) = v_0(x),\\ \\ x\\in \\Omega, \\end{array}\\right.$$ where $\\Omega\\subset\\mathbb{R}^N(N\\geq1)$ is a bounded domain with smooth boundary $\\partial\\Omega,$ $\\chi>0$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03544","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"}