{"paper":{"title":"Existence of Neumann and singular 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":"2014-06-11T04:50:28Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\R^n$, $n\\ge 3$, $0<m\\le\\frac{n-2}{n}$, $a_1,a_2,..., a_{i_0}\\in\\Omega$, $\\delta_0=\\min_{1\\le i\\le i_0}{dist }(a_i,\\1\\Omega)$ and let $\\Omega_{\\delta}=\\Omega\\setminus\\cup_{i=1}^{i_0}B_{\\delta}(a_i)$ and $\\hat{\\Omega}=\\Omega\\setminus\\{a_1\\,...,a_{i_0}\\}$. For any $0<\\delta<\\delta_0$ we will prove the existence and uniqueness of positive solution of the Neumann problem for the equation $u_t=\\Delta u^m$ in $\\Omega_{\\delta}\\times (0,T)$ for some $T>0$. We will prove the existence of singular solutions of this equation in $\\hat{\\Omega}\\times (0,T)$ for so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2776","kind":"arxiv","version":4},"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"}