{"paper":{"title":"Boundedness and stabilization in a two-species chemotaxis-competition system of parabolic-parabolic-elliptic type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami","submitted_at":"2017-03-24T12:42:21Z","abstract_excerpt":"This paper deals with the two-species chemotaxis-competition system $u_t = d_1 \\Delta u - \\chi_1 \\nabla \\cdot (u \\nabla w) + \\mu_1 u(1 - u - a_1 v)$, $v_t = d_2 \\Delta v - \\chi_2 \\nabla \\cdot (v \\nabla w) + \\mu_2 v(1 - a_2 u - v)$, $0 = d_3 \\Delta w + \\alpha u + \\beta v - \\gamma w$, where $\\Omega$ is a bounded domain in $\\mathbb{R}^n$ with smooth boundary, $n\\ge 2$; $\\chi_i$ and $\\mu_i$ are constants satisfying some conditions. The above system was studied in the cases that $a_1,a_2\\in (0,1)$ and $a_1>1>a_2$, and it was proved that global existence and asymptotic stability hold when $\\frac{\\ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08389","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"}