{"paper":{"title":"Extinction of solutions to a class of fast diffusion systems with nonlinear sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenjie Gao, Yuzhu Han","submitted_at":"2013-12-21T11:40:05Z","abstract_excerpt":"In this paper, the finite time extinction of solutions to the fast diffusion system $u_t=\\mathrm{div}(|\\nabla u|^{p-2}\\nabla u)+v^m$, $v_t=\\mathrm{div}(|\\nabla v|^{q-2}\\nabla v)+u^n$ is investigated, where $1<p,q<2$, $m,n>0$ and $\\Omega\\subset \\mathbb{R}^N\\ (N\\geq1)$ is a bounded smooth domain. After establishing the local existence of weak solutions, the authors show that if $mn>(p-1)(q-1)$, then any solution vanishes in finite time provided that the initial data are ``comparable\"; if $mn=(p-1)(q-1)$ and $\\Omega$ is suitably small, then the existence of extinction solutions for small initial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6243","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"}