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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.0700","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-03T11:02:06Z","cross_cats_sorted":[],"title_canon_sha256":"1a37f41b275c9172a869b4f6caaf4d21dae41dba3faff4d94a55093d6d4b1170","abstract_canon_sha256":"ff3b4e39e6362124e352256500d01a8bc5cd1f2ee91e24f4942cbe601ef18f4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:16.257421Z","signature_b64":"bnLTG/v/Ip0Eq5ftRbT7nKW48FS5+UDfbx5pd7u81JSDFPEbA6C5YKMfHhOmnnPQrZKLp2vb6IRy1PabnfiCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6ba8243cb64c7dca1c60ddd63a4b6e47d56483d60579bfdc94a642972e2b629","last_reissued_at":"2026-05-18T02:23:16.256888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:16.256888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $m_s=(d-2)_+/(d+2)<m<1$. 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