{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:B5FPWCEVI6G4TMUPVDAPGZUK6X","short_pith_number":"pith:B5FPWCEV","schema_version":"1.0","canonical_sha256":"0f4afb0895478dc9b28fa8c0f3668af5f7ab38cb0d7a7aeb2a1decf265e08c81","source":{"kind":"arxiv","id":"1811.04410","version":1},"attestation_state":"computed","paper":{"title":"Vanishing time behavior of solutions to the fast diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui, Soojung Kim","submitted_at":"2018-11-11T13:16:26Z","abstract_excerpt":"Let $n\\geq 3$, $0< m<\\frac{n-2}{n}$ and $T>0$. We construct positive solutions to the fast diffusion equation $u_t=\\Delta u^m$ in $\\mathbb{R}^n\\times(0,T)$, which vanish at time $T$. By introducing a scaling parameter $\\beta$ inspired by \\cite{DKS}, we study the second-order asymptotics of the self-similar solutions associated with $\\beta$ at spatial infinity. We also investigate the asymptotic behavior of the solutions to the fast diffusion equation near the vanishing time $T$, provided that the initial value of the solution is close to the initial value of some self-similar solution and sati"},"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":"1811.04410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-11T13:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"7876bf884873d9da02d266782e406064454eaead41ca8b58e8f3234f639d7eed","abstract_canon_sha256":"cebaa5d827226580271dd4fc924ca3edd17a80595b38870a16a597feb4629926"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:05.252821Z","signature_b64":"C9Pa9ek+8WAB8zOjnCYk5d3jbflLwUuNIL99cJ53NsMysn1lgAaDjG7fr4G8kvKfa6WYIxC1qN7q+cdz4ciGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f4afb0895478dc9b28fa8c0f3668af5f7ab38cb0d7a7aeb2a1decf265e08c81","last_reissued_at":"2026-05-18T00:01:05.252167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:05.252167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing time behavior of solutions to the fast diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui, Soojung Kim","submitted_at":"2018-11-11T13:16:26Z","abstract_excerpt":"Let $n\\geq 3$, $0< m<\\frac{n-2}{n}$ and $T>0$. We construct positive solutions to the fast diffusion equation $u_t=\\Delta u^m$ in $\\mathbb{R}^n\\times(0,T)$, which vanish at time $T$. By introducing a scaling parameter $\\beta$ inspired by \\cite{DKS}, we study the second-order asymptotics of the self-similar solutions associated with $\\beta$ at spatial infinity. We also investigate the asymptotic behavior of the solutions to the fast diffusion equation near the vanishing time $T$, provided that the initial value of the solution is close to the initial value of some self-similar solution and sati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04410","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.04410","created_at":"2026-05-18T00:01:05.252272+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.04410v1","created_at":"2026-05-18T00:01:05.252272+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04410","created_at":"2026-05-18T00:01:05.252272+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5FPWCEVI6G4","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5FPWCEVI6G4TMUP","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5FPWCEV","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X","json":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X.json","graph_json":"https://pith.science/api/pith-number/B5FPWCEVI6G4TMUPVDAPGZUK6X/graph.json","events_json":"https://pith.science/api/pith-number/B5FPWCEVI6G4TMUPVDAPGZUK6X/events.json","paper":"https://pith.science/paper/B5FPWCEV"},"agent_actions":{"view_html":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X","download_json":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X.json","view_paper":"https://pith.science/paper/B5FPWCEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.04410&json=true","fetch_graph":"https://pith.science/api/pith-number/B5FPWCEVI6G4TMUPVDAPGZUK6X/graph.json","fetch_events":"https://pith.science/api/pith-number/B5FPWCEVI6G4TMUPVDAPGZUK6X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X/action/storage_attestation","attest_author":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X/action/author_attestation","sign_citation":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X/action/citation_signature","submit_replication":"https://pith.science/pith/B5FPWCEVI6G4TMUPVDAPGZUK6X/action/replication_record"}},"created_at":"2026-05-18T00:01:05.252272+00:00","updated_at":"2026-05-18T00:01:05.252272+00:00"}