{"paper":{"title":"Finite-time blow-up in a quasilinear degenerate chemotaxis system with flux limitation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masaaki Mizukami, Tomomi Yokota, Yuka Chiyoda","submitted_at":"2019-03-01T02:01:29Z","abstract_excerpt":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{align*} \\begin{cases} u_t = \\nabla\\cdot\\left(\\dfrac{u^p \\nabla u}{\\sqrt{u^2 + |\\nabla u|^2}} \\right) -\\chi \\nabla\\cdot\\left( \\dfrac{u^q\\nabla v}{\\sqrt{1 + |\\nabla v|^2}}\\right), &x\\in \\Omega,\\ t>0, \\\\[1mm] 0 = \\Delta v - \\mu + u, &x\\in \\Omega,\\ t>0, \\end{cases} \\end{align*} where $\\Omega := B_R(0) \\subset \\mathbb{R}^n$ ($n \\in \\mathbb{N}$) is a ball with some $R>0$, and $\\chi >0$, $p,q\\geq1$, $\\mu := \\frac 1{|\\Omega|} \\int_\\Omega u_0$ and $u_0$ is an initial data of an unknown function $u$. Bellomo--"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00125","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"}