{"paper":{"title":"Existence and large time behaviour of finite points blow-up solutions of the fast diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui, SungHoon Kim","submitted_at":"2017-12-15T03:13:25Z","abstract_excerpt":"Let $\\Omega\\subset\\R^n$ be a smooth bounded domain and let $a_1,a_2,\\dots,a_{i_0}\\in\\Omega$, $\\widehat{\\Omega}=\\Omega\\setminus\\{a_1,a_2,\\dots,a_{i_0}\\}$ and $\\widehat{R^n}=\\R^n\\setminus\\{a_1,a_2,\\dots,a_{i_0}\\}$. We prove the existence of solution $u$ of the fast diffusion equation $u_t=\\Delta u^m$, $u>0$, in $\\widehat{\\Omega}\\times (0,\\infty)$ ($\\widehat{R^n}\\times (0,\\infty)$ respectively) which satisfies $u(x,t)\\to\\infty$ as $x\\to a_i$ for any $t>0$ and $i=1,\\cdots,i_0$, when $0<m<\\frac{n-2}{n}$, $n\\geq 3$, and the initial value satisfies $0\\le u_0\\in L^p_{loc}(\\2{\\Omega}\\setminus\\{a_1,\\cdo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05515","kind":"arxiv","version":2},"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"}