{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HYOTLOFHGIZJFV7QSUGAHR5EWT","short_pith_number":"pith:HYOTLOFH","schema_version":"1.0","canonical_sha256":"3e1d35b8a7323292d7f0950c03c7a4b4c01789d59608aef809b334e317ade4a4","source":{"kind":"arxiv","id":"1810.02161","version":1},"attestation_state":"computed","paper":{"title":"Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georgy Kitavtsev, Roman M. Taranets","submitted_at":"2018-10-04T11:58:00Z","abstract_excerpt":"In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory."},"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":"1810.02161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-04T11:58:00Z","cross_cats_sorted":[],"title_canon_sha256":"ac815304510ec1d753148dc77577ff78fb9120177bc808a23df6d8a0a213a9b4","abstract_canon_sha256":"19bbbbd0242167a7719fdca9b085977114291ee58bffda78b7af838c02c35e81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:06.062812Z","signature_b64":"3tLwPlJMKNlUfFlXIVr0ynoMrNfxyCWh+7M1qUXMyIhyx6eIalsTtROr4XqbJ4VdzWLP2IYCRgUtKrOCgoAyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e1d35b8a7323292d7f0950c03c7a4b4c01789d59608aef809b334e317ade4a4","last_reissued_at":"2026-05-18T00:04:06.062128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:06.062128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georgy Kitavtsev, Roman M. Taranets","submitted_at":"2018-10-04T11:58:00Z","abstract_excerpt":"In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02161","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":"1810.02161","created_at":"2026-05-18T00:04:06.062223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.02161v1","created_at":"2026-05-18T00:04:06.062223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02161","created_at":"2026-05-18T00:04:06.062223+00:00"},{"alias_kind":"pith_short_12","alias_value":"HYOTLOFHGIZJ","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HYOTLOFHGIZJFV7Q","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HYOTLOFH","created_at":"2026-05-18T12:32:28.185984+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/HYOTLOFHGIZJFV7QSUGAHR5EWT","json":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT.json","graph_json":"https://pith.science/api/pith-number/HYOTLOFHGIZJFV7QSUGAHR5EWT/graph.json","events_json":"https://pith.science/api/pith-number/HYOTLOFHGIZJFV7QSUGAHR5EWT/events.json","paper":"https://pith.science/paper/HYOTLOFH"},"agent_actions":{"view_html":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT","download_json":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT.json","view_paper":"https://pith.science/paper/HYOTLOFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.02161&json=true","fetch_graph":"https://pith.science/api/pith-number/HYOTLOFHGIZJFV7QSUGAHR5EWT/graph.json","fetch_events":"https://pith.science/api/pith-number/HYOTLOFHGIZJFV7QSUGAHR5EWT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT/action/storage_attestation","attest_author":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT/action/author_attestation","sign_citation":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT/action/citation_signature","submit_replication":"https://pith.science/pith/HYOTLOFHGIZJFV7QSUGAHR5EWT/action/replication_record"}},"created_at":"2026-05-18T00:04:06.062223+00:00","updated_at":"2026-05-18T00:04:06.062223+00:00"}