{"paper":{"title":"Explicit lower bound of blow--up time for an attraction--repulsion chemotaxis system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Viglialoro","submitted_at":"2019-03-19T18:15:50Z","abstract_excerpt":"In this paper we study classical solutions to the zero--flux attraction--repulsion chemotaxis--system \\begin{equation}\\label{ProblemAbstract} \\tag{$\\Diamond$} \\begin{cases} u_{ t}=\\Delta u -\\chi \\nabla \\cdot (u\\nabla v)+\\xi \\nabla \\cdot (u\\nabla w) & \\textrm{in }\\Omega\\times (0,t^*), \\\\ 0=\\Delta v+\\alpha u-\\beta v & \\textrm{in } \\Omega\\times (0,t^*),\\\\ 0=\\Delta w+\\gamma u-\\delta w & \\textrm{in } \\Omega\\times (0,t^*),\\\\ \\end{cases} \\end{equation} where $\\Omega$ is a smooth and bounded domain of $\\mathbb{R}^2$, $t^*$ is the blow--up time and $\\alpha,\\beta,\\gamma,\\delta,\\chi,\\xi$ are positive rea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08196","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"}