{"paper":{"title":"Extensibility criterion ruling out gradient 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, Tatsuhiko Ono, Tomomi Yokota","submitted_at":"2019-03-01T01:54:23Z","abstract_excerpt":"This paper deals with the quasilinear degenerate chemotaxis system with flux limitation \\begin{equation*} \\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), \\\\[1mm] 0 = \\Delta v - \\mu + u \\end{cases}\\end{equation*} under no-flux boundary conditions in balls $\\Omega\\subset\\mathbb{R}^n$, and the initial condition $u|_{t=0}=u_0$ for a radially symmetric and positive initial data $u_0\\in C^3(\\overline{\\Omega})$, where $\\chi>0$ and $\\mu:=\\frac{1}{|\\Omega|}\\int_{\\Omega}u_0$. Bellomo-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00124","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"}