{"paper":{"title":"Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Matteo Bonforte","submitted_at":"2019-02-08T16:52:46Z","abstract_excerpt":"We investigate the homogeneous Dirichlet problem for the Fast Diffusion Equation $u_t=\\Delta u^m$, posed in a smooth bounded domain $\\Omega\\subset \\mathbb{R}^N$, in the exponent range $m_s=(N-2)_+/(N+2)<m<1$. It is known that bounded positive solutions extinguish in a finite time $T>0$, and also that they approach a separate variable solution $u(t,x)\\sim (T-t)^{1/(1-m)}S(x)$, as $t\\to T^-$. It has been shown recently that $v(x,t)=u(t,x)\\,(T-t)^{-1/(1-m)}$ tends to $S(x)$ as $t\\to T^-$, uniformly in the relative error norm. Starting from this result, we investigate the fine asymptotic behaviour"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03189","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"}