{"paper":{"title":"Dynamics in chemotaxis models of parabolic-elliptic type on bounded domain with time and space dependent logistic sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tahir Bachar Issa, Wenxian Shen","submitted_at":"2016-09-03T05:03:34Z","abstract_excerpt":"This paper considers the dynamics of the following chemotaxis system $$ \\begin{cases} u_t=\\Delta u-\\chi\\nabla (u\\cdot \\nabla v)+u\\left(a_0(t,x)-a_1(t,x)u-a_2(t,x)\\int_{\\Omega}u\\right),\\quad x\\in \\Omega\\cr 0=\\Delta v+ u-v,\\quad x\\in \\Omega \\quad \\cr \\frac{\\partial u}{\\partial n}=\\frac{\\partial v}{\\partial n}=0,\\quad x\\in\\partial\\Omega, \\end{cases} $$ where $\\Omega \\subset \\mathbb{R}^n(n\\geq 1)$ is a bounded domain with smooth boundary $\\partial\\Omega$ and $a_i(t,x)$ ($i=0,1,2$) are locally H\\\"older continuous in $t\\in\\mathbb{R}$ uniformly with respect to $x\\in\\bar{\\Omega}$ and continuous in $x\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00794","kind":"arxiv","version":3},"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"}