{"paper":{"title":"Boundedness of solution of a parabolic--ODE--parabolic chemotaxis--haptotaxis model with (generalized) logistic source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiashan Zheng","submitted_at":"2017-11-27T23:49:56Z","abstract_excerpt":"In this paper, we study the following chemotaxis--haptotaxis system with (generalized) logistic source $$\n  \\left\\{\\begin{array}{ll}\n  u_t=\\Delta u-\\chi\\nabla\\cdot(u\\nabla v)-\n  \\xi\\nabla\\cdot(u\\nabla w)+u(a-\\mu u^{r-1}-w),\n  \\displaystyle{v_t=\\Delta v- v +u},\\quad \\\\ \\displaystyle{w_t=- vw},\\quad\\\\ \\displaystyle{\\frac{\\partial u}{\\partial \\nu}=\\frac{\\partial v}{\\partial \\nu}=\\frac{\\partial w}{\\partial \\nu}=0},\\quad x\\in \\partial\\Omega, t>0,\\\\ \\displaystyle{u(x,0)=u_0(x)},v(x,0)=v_0(x),w(x,0)=w_0(x),\\quad x\\in \\Omega,\n  \\end{array}\\right.\\eqno(0.1) $$ %under homogeneous Neumann boundary condit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10048","kind":"arxiv","version":2},"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"}