{"paper":{"title":"Sharp extinction rates for positive solutions of fast diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Meng Yu, Tobias K\\\"onig","submitted_at":"2024-11-07T15:22:43Z","abstract_excerpt":"Let $s \\in (0, 1]$ and $N > 2s$. It is known that positive solutions to the (fractional) fast diffusion equation $\\partial_t u + (-\\Delta)^s (u^\\frac{N-2s}{N+2s}) = 0$ on $(0, \\infty) \\times \\mathbb R^N$ with regular enough initial datum extinguish after some finite time $T_* > 0$. More precisely, one has $\\frac{u(t,\\cdot)}{U_{T_*, z, \\lambda}(t,\\cdot)} - 1 =o(1)$ as $t \\to T_*^-$ for a certain extinction profile $U_{T_*, z, \\lambda}$, uniformly on $\\mathbb R^N$. In this paper, we prove the quantitative bound $ \\frac{u(t,\\cdot)}{U_{T_*, z, \\lambda}(t,\\cdot)} - 1 = \\mathcal O( (T_*-t)^\\frac{N+2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.04783","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.04783/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}