{"paper":{"title":"Boundedness and exponential convergence of a chemotaxis model for tumor invasion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haiyang Jin, Tian Xiang","submitted_at":"2016-04-13T18:13:23Z","abstract_excerpt":"We revisit the following chemotaxis system modeling tumor invasion \\begin{equation*} \\begin{cases} u_t=\\Delta u-\\nabla \\cdot(u\\nabla v),& x\\in\\Omega, t>0,\\\\ v_t=\\Delta v+wz,& x\\in\\Omega, t>0,\\\\ w_t=-wz,& x\\in\\Omega, t>0,\\\\ z_t=\\Delta z-z+u, & x\\in\\Omega, t>0,\\\\ \\end{cases} \\end{equation*} in a smooth bounded domain $\\Omega \\subset \\mathbb{R}^n(n\\geq 1)$ with homogeneous Neumann boundary and initial conditions. This model was recently proposed by Fujie et al. \\cite{FIY14} as a model for tumor invasion with the role of extracellular matrix incorporated, and was analyzed by Fujie et al. \\cite{FIW"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03898","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"}