{"paper":{"title":"Global solvability and boundedness in the $N$-dimensional quasilinear chemotaxis model with logistic source and consumption of chemoattractant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2018-01-05T14:55:20Z","abstract_excerpt":"We consider the following chemotaxis model %fully parabolic Keller-Segel system with logistic source $$ \\left\\{\\begin{array}{ll} u_t=\\nabla\\cdot(D(u)\\nabla u)-\\chi\\nabla\\cdot(u\\nabla v)+\\mu (u-u^2),\\quad x\\in \\Omega, t>0, \\disp{v_t-\\Delta v=-uv },\\quad x\\in \\Omega, t>0, %\\disp{\\tau w_t+\\delta w=u },\\quad %x\\in \\Omega, t>0, \\disp{(\\nabla D(u)-\\chi u\\cdot \\nabla v)\\cdot \\nu=\\frac{\\partial v}{\\partial\\nu}=0},\\quad x\\in \\partial\\Omega, t>0, \\disp{u(x,0)=u_0(x)},\\quad v(x,0)=v_0(x),~~ x\\in \\Omega \\end{array}\\right. $$ on a bounded domain $\\Omega\\subset\\mathbb{R}^N(N\\geq1)$, with smooth boundary $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01774","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"}