{"paper":{"title":"A refined criterion and lower bounds for the blow--up time in a parabolic--elliptic chemotaxis system with nonlinear diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Viglialoro, Monica Marras, Teruto Nishino","submitted_at":"2019-04-08T06:09:00Z","abstract_excerpt":"This paper deals with unbounded solutions to the following zero--flux chemotaxis system \\begin{equation}\\label{ProblemAbstract} \\tag{$\\Diamond$}\n  \\begin{cases}\n  % about u\n  u_t=\\nabla \\cdot [(u+\\alpha)^{m_1-1}\n  \\nabla u-\\chi u(u+\\alpha)^{m_2-2}\n  \\nabla v]\n  &\n  (x,t) \\in \\Omega \\times (0,T_{max}),\n  \\\\[1mm]\n  % about v\n  0=\\Delta v-M+u\n  &\n  (x,t) \\in \\Omega \\times (0,T_{max}),\n  \\end{cases} \\end{equation} where $\\alpha>0$, $\\Omega$ is a smooth and bounded domain of $\\mathbb{R}^n$, with $n\\geq 1$, $t\\in (0, T_{max})$, where $T_{max}$ the blow-up time, and $m_1,m_2$ real numbers. Given a su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03856","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"}