{"paper":{"title":"Asymptotic large time behavior of 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, Soojung Kim","submitted_at":"2015-08-09T03:09:21Z","abstract_excerpt":"We study the asymptotic large time behavior of singular solutions of the fast diffusion equation $u_t=\\Delta u^m$ in $({\\mathbb R}^n\\setminus\\{0\\})\\times(0,\\infty)$ in the subcritical case $0<m<\\frac{n-2}{n}$, $n\\ge3$. Firstly, we prove the existence of singular solution $u$ of the above equation that is trapped in between self-similar solutions of the form of $t^{-\\alpha} f_i(t^{-\\beta}x)$, $i=1,2$, with initial value $u_0$ satisfying $A_1|x|^{-\\gamma}\\le u_0\\le A_2|x|^{-\\gamma}$ for some constants $A_2>A_1>0$ and $\\frac{2}{1-m}<\\gamma<\\frac{n-2}{m}$, where $\\beta:=\\frac{1}{2-\\gamma(1-m)}$, $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01980","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"}