{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6LV6SRJPGTHCIDSK3CTLDPJDUV","short_pith_number":"pith:6LV6SRJP","schema_version":"1.0","canonical_sha256":"f2ebe9452f34ce240e4ad8a6b1bd23a56ccabf51712fa544e9ee0535ebc0609c","source":{"kind":"arxiv","id":"1410.4079","version":1},"attestation_state":"computed","paper":{"title":"Blow-up results for a strongly perturbed semilinear heat equation: Theoretical analysis and numerical method","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Van Tien Nguyen","submitted_at":"2014-10-15T14:52:09Z","abstract_excerpt":"We consider a blow-up solution for a strongly perturbed semilinear heat equation with Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for the problem. Using this Lyapunov functional, we derive the blow-up rate and the blow-up limit of the solution. We also classify all asymptotic behaviors of the solution at the singularity and give precisely blow-up profiles corresponding to these behaviors. Finally, we attain the blow-up profile numerically, thanks to a new mesh-refinement algorithm inspired by the rescaling method of Be"},"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":"1410.4079","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2014-10-15T14:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"743b1803f4757df5581f29d8e41dbedaa93f0058bab4606e783e1ecd71598423","abstract_canon_sha256":"d6fab24d6f810ebd07c2e3daa441d58cc3c97a3b370f83da47bd7e8150a64df2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:12.225413Z","signature_b64":"7ItoFr+x/n6Wr33ki8iQaG8M3xAIa+YWAMxlJmfFhU2IxazrLEGD5+UZb2aKbuJK1XBkLUEYBE01MU8quflNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2ebe9452f34ce240e4ad8a6b1bd23a56ccabf51712fa544e9ee0535ebc0609c","last_reissued_at":"2026-05-18T01:20:12.224824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:12.224824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blow-up results for a strongly perturbed semilinear heat equation: Theoretical analysis and numerical method","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Van Tien Nguyen","submitted_at":"2014-10-15T14:52:09Z","abstract_excerpt":"We consider a blow-up solution for a strongly perturbed semilinear heat equation with Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for the problem. Using this Lyapunov functional, we derive the blow-up rate and the blow-up limit of the solution. We also classify all asymptotic behaviors of the solution at the singularity and give precisely blow-up profiles corresponding to these behaviors. Finally, we attain the blow-up profile numerically, thanks to a new mesh-refinement algorithm inspired by the rescaling method of Be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4079","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":"1410.4079","created_at":"2026-05-18T01:20:12.224907+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.4079v1","created_at":"2026-05-18T01:20:12.224907+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4079","created_at":"2026-05-18T01:20:12.224907+00:00"},{"alias_kind":"pith_short_12","alias_value":"6LV6SRJPGTHC","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6LV6SRJPGTHCIDSK","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6LV6SRJP","created_at":"2026-05-18T12:28:16.859392+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/6LV6SRJPGTHCIDSK3CTLDPJDUV","json":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV.json","graph_json":"https://pith.science/api/pith-number/6LV6SRJPGTHCIDSK3CTLDPJDUV/graph.json","events_json":"https://pith.science/api/pith-number/6LV6SRJPGTHCIDSK3CTLDPJDUV/events.json","paper":"https://pith.science/paper/6LV6SRJP"},"agent_actions":{"view_html":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV","download_json":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV.json","view_paper":"https://pith.science/paper/6LV6SRJP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.4079&json=true","fetch_graph":"https://pith.science/api/pith-number/6LV6SRJPGTHCIDSK3CTLDPJDUV/graph.json","fetch_events":"https://pith.science/api/pith-number/6LV6SRJPGTHCIDSK3CTLDPJDUV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV/action/storage_attestation","attest_author":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV/action/author_attestation","sign_citation":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV/action/citation_signature","submit_replication":"https://pith.science/pith/6LV6SRJPGTHCIDSK3CTLDPJDUV/action/replication_record"}},"created_at":"2026-05-18T01:20:12.224907+00:00","updated_at":"2026-05-18T01:20:12.224907+00:00"}