{"paper":{"title":"Boundedness in a two-dimensional chemotaxis-haptotaxis system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Youshan Tao","submitted_at":"2014-07-28T11:20:06Z","abstract_excerpt":"This work studies the chemotaxis-haptotaxis system\n  $$\\left\\{ \\begin{array}{ll} u_t= \\Delta u - \\chi \\nabla \\cdot (u\\nabla v) - \\xi \\nabla \\cdot (u\\nabla w) + \\mu u(1-u-w), &\\qquad x\\in \\Omega, \\, t>0, \\\\[1mm]\n  v_t=\\Delta v-v+u, &\\qquad x\\in \\Omega, \\, t>0, \\\\[1mm]\n  w_t=-vw, &\\qquad x\\in \\Omega, \\, t>0, \\end{array} \\right. $$\n   in a bounded smooth domain $\\Omega\\subset\\mathbb{R}^2$ with zero-flux boundary conditions, where the parameters $\\chi, \\xi$ and $\\mu$ are assumed to be positive. It is shown that under appropriate regularity assumption on the initial data $(u_0, v_0, w_0)$, the corr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7382","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"}