{"paper":{"title":"Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Johannes Lankeit, Yulan Wang","submitted_at":"2016-08-29T10:52:40Z","abstract_excerpt":"This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \\begin{eqnarray*} \\begin{array}{llc} u_t=\\Delta u-\\chi\\nabla\\cdot (u\\nabla v)+\\kappa u-\\mu u^2,\\\\ v_t=\\Delta v-uv,\n  \\end{array} \\end{eqnarray*} in $N$-dimensional bounded smooth domains for suitably regular positive initial data.\n  We shall establish the existence of a global bounded classical solution for suitably large $\\mu$ and prove that for any $\\mu>0$ there exists a weak solution.\n  Moreover, in the case of $\\kappa>0$ convergence to the constant equilibrium $(\\frac{\\kappa}{\\mu},0)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07991","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"}