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We prove the existence of solution $u$ of the fast diffusion equation $u_t=\\Delta u^m$, $u>0$, in $\\widehat{\\Omega}\\times (0,\\infty)$ ($\\widehat{R^n}\\times (0,\\infty)$ respectively) which satisfies $u(x,t)\\to\\infty$ as $x\\to a_i$ for any $t>0$ and $i=1,\\cdots,i_0$, when $0<m<\\frac{n-2}{n}$, $n\\geq 3$, and the initial value satisfies $0\\le u_0\\in L^p_{loc}(\\2{\\Omega}\\setminus\\{a_1,\\cdo"},"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":"1712.05515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-15T03:13:25Z","cross_cats_sorted":[],"title_canon_sha256":"4b2f56c0a7363bf61b312e41666964ff730b6eb7a423da94f266df45ab7f8a1d","abstract_canon_sha256":"a5632d98f558259b42c84680399b143897dfe625c768ac23d6f6442e0004a176"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:55.892938Z","signature_b64":"A1c1i8Un6VbtwaIwOMSGnfBokkMn9neKHSCavjtuO7wTdEEugZ+RoXZRkly7L4UN19J+WEdmubnwyHhipiMuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ac411f28b4fcc808d1693c33249ed868ab438bb915ebebb1856db271a7d55a8","last_reissued_at":"2026-05-18T00:16:55.892186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:55.892186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and large time behaviour of finite points blow-up solutions of 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, SungHoon Kim","submitted_at":"2017-12-15T03:13:25Z","abstract_excerpt":"Let $\\Omega\\subset\\R^n$ be a smooth bounded domain and let $a_1,a_2,\\dots,a_{i_0}\\in\\Omega$, $\\widehat{\\Omega}=\\Omega\\setminus\\{a_1,a_2,\\dots,a_{i_0}\\}$ and $\\widehat{R^n}=\\R^n\\setminus\\{a_1,a_2,\\dots,a_{i_0}\\}$. We prove the existence of solution $u$ of the fast diffusion equation $u_t=\\Delta u^m$, $u>0$, in $\\widehat{\\Omega}\\times (0,\\infty)$ ($\\widehat{R^n}\\times (0,\\infty)$ respectively) which satisfies $u(x,t)\\to\\infty$ as $x\\to a_i$ for any $t>0$ and $i=1,\\cdots,i_0$, when $0<m<\\frac{n-2}{n}$, $n\\geq 3$, and the initial value satisfies $0\\le u_0\\in L^p_{loc}(\\2{\\Omega}\\setminus\\{a_1,\\cdo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05515","kind":"arxiv","version":2},"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":"1712.05515","created_at":"2026-05-18T00:16:55.892307+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.05515v2","created_at":"2026-05-18T00:16:55.892307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05515","created_at":"2026-05-18T00:16:55.892307+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLCBD4ULJ7GI","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLCBD4ULJ7GIBDIW","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLCBD4UL","created_at":"2026-05-18T12:31:15.632608+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/FLCBD4ULJ7GIBDIWSPBTESPNQ2","json":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2.json","graph_json":"https://pith.science/api/pith-number/FLCBD4ULJ7GIBDIWSPBTESPNQ2/graph.json","events_json":"https://pith.science/api/pith-number/FLCBD4ULJ7GIBDIWSPBTESPNQ2/events.json","paper":"https://pith.science/paper/FLCBD4UL"},"agent_actions":{"view_html":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2","download_json":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2.json","view_paper":"https://pith.science/paper/FLCBD4UL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.05515&json=true","fetch_graph":"https://pith.science/api/pith-number/FLCBD4ULJ7GIBDIWSPBTESPNQ2/graph.json","fetch_events":"https://pith.science/api/pith-number/FLCBD4ULJ7GIBDIWSPBTESPNQ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2/action/storage_attestation","attest_author":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2/action/author_attestation","sign_citation":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2/action/citation_signature","submit_replication":"https://pith.science/pith/FLCBD4ULJ7GIBDIWSPBTESPNQ2/action/replication_record"}},"created_at":"2026-05-18T00:16:55.892307+00:00","updated_at":"2026-05-18T00:16:55.892307+00:00"}