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For any $\\lambda>0$, we will prove the existence and uniqueness (for $\\beta\\ge\\frac{\\rho_1}{n-2-nm}$) of radially symmetric singular solution $g_{\\lambda}\\in C^{\\infty}(R^n\\setminus\\{0\\})$ of the elliptic equation $\\Delta v^m+\\alpha v+\\beta x\\cdot\\nabla v=0$, $v>0$, in $R^n\\setminus\\{0\\}$, satisfying $\\displaystyle\\lim_{|x|\\to 0}|x|^{\\alpha/\\beta}g_{\\lambda}(x)=\\lambda^{-\\frac{\\rho_1}{(1-m)\\beta}}$. When $\\beta$ is sufficiently large, we prove the higher order asymptotic beha"},"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":"1407.2696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-10T05:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"5d81a36dfad39fc84956f1967e4c55b053acc840cd7a7bd803eec758917b0894","abstract_canon_sha256":"dbf7b952ce3b2e03268d8d70bb8d432c918fe7ceedb0deeb1f58913b19c00efc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:47.183095Z","signature_b64":"RvB3Xf53s3fm+BngBbCzdyjE3D4kk7fNSghVs0uC1fqCP/enaf7tIh5GaoxuCQy+ncp4mxvRfhmwSt28pHy4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f07a47c7c0f073e816c2d9bbcb934e85ad7f465c129dbf99f5b44db20862e296","last_reissued_at":"2026-05-18T02:35:47.182711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:47.182711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic behaviour of solutions of the fast diffusion equation near its extinction time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui","submitted_at":"2014-07-10T05:37:13Z","abstract_excerpt":"Let $n\\ge 3$, $0<m<\\frac{n-2}{n}$, $\\rho_1>0$, $\\beta\\ge\\frac{m\\rho_1}{n-2-nm}$ and $\\alpha=\\frac{2\\beta+\\rho_1}{1-m}$. For any $\\lambda>0$, we will prove the existence and uniqueness (for $\\beta\\ge\\frac{\\rho_1}{n-2-nm}$) of radially symmetric singular solution $g_{\\lambda}\\in C^{\\infty}(R^n\\setminus\\{0\\})$ of the elliptic equation $\\Delta v^m+\\alpha v+\\beta x\\cdot\\nabla v=0$, $v>0$, in $R^n\\setminus\\{0\\}$, satisfying $\\displaystyle\\lim_{|x|\\to 0}|x|^{\\alpha/\\beta}g_{\\lambda}(x)=\\lambda^{-\\frac{\\rho_1}{(1-m)\\beta}}$. 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