{"paper":{"title":"Behaviour near extinction for the Fast Diffusion Equation on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabriele Grillo, Juan Luis Vazquez, Matteo Bonforte","submitted_at":"2010-12-03T11:02:06Z","abstract_excerpt":"We consider the Fast Diffusion Equation $u_t=\\Delta u^m$ posed in a bounded smooth domain $\\Omega\\subset \\RR^d$ with homogeneous Dirichlet conditions; the exponent range is $m_s=(d-2)_+/(d+2)<m<1$. It is known that bounded positive solutions $u(t,x)$ of such problem extinguish in a finite time $T$, and also that such solutions approach a separate variable solution $u(t,x)\\sim (T-t)^{1/(1-m)}S(x)$, as $t\\to T^-$. Here we are interested in describing the behaviour of the solutions near the extinction time. We first show that the convergence $u(t,x)\\,(T-t)^{-1/(1-m)}$ to $S(x)$ takes place unifor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0700","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"}