{"paper":{"title":"Effect of nonlinear diffusion on a lower bound for the blow-up time in a fully parabolic chemotaxis system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Teruto Nishino, Tomomi Yokota","submitted_at":"2019-02-26T08:12:49Z","abstract_excerpt":"This paper deals with a lower bound for the blow-up time for solutions of the fully parabolic chemotaxis system \\begin{equation*}\n  \\begin{cases}\n  u_t=\\nabla \\cdot [(u+\\alpha)^{m_1-1}\n  \\nabla u-\\chi u(u+\\alpha)^{m_2-2}\n  \\nabla v]\n  & {\\rm in} \\; \\Omega \\times (0,T), \\\\[1mm]\n  v_t=\\Delta v-v+u\n  & {\\rm in} \\; \\Omega \\times (0,T)\n  \\end{cases} \\end{equation*} under Neumann boundary conditions and initial conditions, where $\\Omega$ is a general bounded domain in $\\mathbb{R}^n$ with smooth boundary, $\\alpha>0$, $\\chi>0$, $m_1, m_2 \\in \\mathbb{R}$ and $T>0$. Recently, Anderson-Deng (2017) gave a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09787","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"}