{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YK4Y5FAXZK3R47XZECRXI2URJV","short_pith_number":"pith:YK4Y5FAX","schema_version":"1.0","canonical_sha256":"c2b98e9417cab71e7ef920a3746a914d4087f342e6713cdcf9e7c29548c4db88","source":{"kind":"arxiv","id":"1509.02719","version":1},"attestation_state":"computed","paper":{"title":"Blow-up in reaction-diffusion systems under Robin boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li-Chang Hung","submitted_at":"2015-09-09T10:54:26Z","abstract_excerpt":"In this paper we apply the differential inequality technique of Payne {\\it et. al} \\cite{Payne&SchaeferRobin08} to show that a reaction-diffusion system admits blow-up solutions, and to determine an upper bound for the blow-up time. For a particular nonlinearity, a lower bound on the blow-up time, when blow-up does occur, is also given."},"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":"1509.02719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-09T10:54:26Z","cross_cats_sorted":[],"title_canon_sha256":"da01763cd5440d7a7bdf5718e82a0707d9df0bbf1d62a96b8979e432e12d5ee9","abstract_canon_sha256":"486ff92aa1da4d14e6681373391711b9cf99609e93eaa0534cb84b3fc5cbf282"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:33.466850Z","signature_b64":"4z24zWhJUfgTOA81I/Bi/PnPYsd7ZMAyNGeISey/g/kLYpIVNgjssf0a7ES1/A1NbWyPo4pBkVJhKSIdkb17BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2b98e9417cab71e7ef920a3746a914d4087f342e6713cdcf9e7c29548c4db88","last_reissued_at":"2026-05-18T01:33:33.466237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:33.466237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blow-up in reaction-diffusion systems under Robin boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li-Chang Hung","submitted_at":"2015-09-09T10:54:26Z","abstract_excerpt":"In this paper we apply the differential inequality technique of Payne {\\it et. al} \\cite{Payne&SchaeferRobin08} to show that a reaction-diffusion system admits blow-up solutions, and to determine an upper bound for the blow-up time. For a particular nonlinearity, a lower bound on the blow-up time, when blow-up does occur, is also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02719","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":"1509.02719","created_at":"2026-05-18T01:33:33.466368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02719v1","created_at":"2026-05-18T01:33:33.466368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02719","created_at":"2026-05-18T01:33:33.466368+00:00"},{"alias_kind":"pith_short_12","alias_value":"YK4Y5FAXZK3R","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YK4Y5FAXZK3R47XZ","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YK4Y5FAX","created_at":"2026-05-18T12:29:50.041715+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/YK4Y5FAXZK3R47XZECRXI2URJV","json":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV.json","graph_json":"https://pith.science/api/pith-number/YK4Y5FAXZK3R47XZECRXI2URJV/graph.json","events_json":"https://pith.science/api/pith-number/YK4Y5FAXZK3R47XZECRXI2URJV/events.json","paper":"https://pith.science/paper/YK4Y5FAX"},"agent_actions":{"view_html":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV","download_json":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV.json","view_paper":"https://pith.science/paper/YK4Y5FAX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02719&json=true","fetch_graph":"https://pith.science/api/pith-number/YK4Y5FAXZK3R47XZECRXI2URJV/graph.json","fetch_events":"https://pith.science/api/pith-number/YK4Y5FAXZK3R47XZECRXI2URJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV/action/storage_attestation","attest_author":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV/action/author_attestation","sign_citation":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV/action/citation_signature","submit_replication":"https://pith.science/pith/YK4Y5FAXZK3R47XZECRXI2URJV/action/replication_record"}},"created_at":"2026-05-18T01:33:33.466368+00:00","updated_at":"2026-05-18T01:33:33.466368+00:00"}