{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UMVOQGRMYOTTBAJ5RF4X3UGUD2","short_pith_number":"pith:UMVOQGRM","schema_version":"1.0","canonical_sha256":"a32ae81a2cc3a730813d89797dd0d41e957e70fd8acc0450f23a2953ab2c1bc7","source":{"kind":"arxiv","id":"1206.2492","version":3},"attestation_state":"computed","paper":{"title":"Stability of solutions to nonlinear diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Teemu Lukkari","submitted_at":"2012-06-12T11:29:24Z","abstract_excerpt":"We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit problem with the same data as $m$ varies. Our arguments are elementary and based on a general principle. We use neither regularity theory nor nonlinear semigroups, and our approach applies to e.g. Dirichlet problems in bounded domains and Cauchy problems on the whole space."},"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":"1206.2492","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-12T11:29:24Z","cross_cats_sorted":[],"title_canon_sha256":"fd1a181b933f8e0de59eb0e5d475e417cfb7e902d7fc0fd847d7d2ea88ee8bf4","abstract_canon_sha256":"a4711bcad6435501d2f1c266d3ab75aa1277a359b917ea92b3354651182cc8bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:26.912188Z","signature_b64":"bO9fSJo/IQiQ7yJ28Mt2yUhf6YmYPANtFkWui0033hhDk3PzL4m6aQX8lFjMu/nQXqIaOUtndR5si78JFfwZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a32ae81a2cc3a730813d89797dd0d41e957e70fd8acc0450f23a2953ab2c1bc7","last_reissued_at":"2026-05-18T03:14:26.911682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:26.911682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of solutions to nonlinear diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Teemu Lukkari","submitted_at":"2012-06-12T11:29:24Z","abstract_excerpt":"We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit problem with the same data as $m$ varies. Our arguments are elementary and based on a general principle. We use neither regularity theory nor nonlinear semigroups, and our approach applies to e.g. Dirichlet problems in bounded domains and Cauchy problems on the whole space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2492","kind":"arxiv","version":3},"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":"1206.2492","created_at":"2026-05-18T03:14:26.911769+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.2492v3","created_at":"2026-05-18T03:14:26.911769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2492","created_at":"2026-05-18T03:14:26.911769+00:00"},{"alias_kind":"pith_short_12","alias_value":"UMVOQGRMYOTT","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UMVOQGRMYOTTBAJ5","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UMVOQGRM","created_at":"2026-05-18T12:27:23.164592+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/UMVOQGRMYOTTBAJ5RF4X3UGUD2","json":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2.json","graph_json":"https://pith.science/api/pith-number/UMVOQGRMYOTTBAJ5RF4X3UGUD2/graph.json","events_json":"https://pith.science/api/pith-number/UMVOQGRMYOTTBAJ5RF4X3UGUD2/events.json","paper":"https://pith.science/paper/UMVOQGRM"},"agent_actions":{"view_html":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2","download_json":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2.json","view_paper":"https://pith.science/paper/UMVOQGRM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.2492&json=true","fetch_graph":"https://pith.science/api/pith-number/UMVOQGRMYOTTBAJ5RF4X3UGUD2/graph.json","fetch_events":"https://pith.science/api/pith-number/UMVOQGRMYOTTBAJ5RF4X3UGUD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2/action/storage_attestation","attest_author":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2/action/author_attestation","sign_citation":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2/action/citation_signature","submit_replication":"https://pith.science/pith/UMVOQGRMYOTTBAJ5RF4X3UGUD2/action/replication_record"}},"created_at":"2026-05-18T03:14:26.911769+00:00","updated_at":"2026-05-18T03:14:26.911769+00:00"}