{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5JTXJV5LXVSH2LW5RAF4TELSV3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9ba9681cf1539536d1a78884700c86efa34150cd116773867987d3110f2b128a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-06T11:37:26Z","title_canon_sha256":"6adad1f5a21a99fbd773ec718707d9a85a587e3ddc08f7a801c53026d295be39"},"schema_version":"1.0","source":{"id":"1210.1941","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1941","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1941v1","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1941","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"5JTXJV5LXVSH","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5JTXJV5LXVSH2LW5","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5JTXJV5L","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:bc7066874233ca83150e99960605822206947d72ecdc1c4344e7e4cb42daac9b","target":"graph","created_at":"2026-05-18T03:08:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is concerned with optimal time-decay estimates of solutions of the Cauchy problem to a model system of the radiating gas in $\\mathbb{R}^n$. Compared to Liu and Kawashima (2011) \\cite{Liu1} and Wang and Wang (2009) \\cite{Wang}, without smallness assumption of initial perturbation in $L^1$-norm, we study large time behavior of small amplitude classical solutions to the Cauchy problem. The optimal $H^N$-norm time-decay rates of the solutions in $\\mathbb{R}^n$ with $1\\leq n\\leq4$ are obtained by applying the Fourier splitting method introduced in Schonbek (1980) \\cite{Schonbek1} with a ","authors_text":"Wenjun Wang, Zhigang Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-06T11:37:26Z","title":"Decay of a model system of radiating gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1941","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3b758cd256c4659bbd4cbc5026e90bbef7974bb7475ff4e46ca7d526109ceefe","target":"record","created_at":"2026-05-18T03:08:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9ba9681cf1539536d1a78884700c86efa34150cd116773867987d3110f2b128a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-06T11:37:26Z","title_canon_sha256":"6adad1f5a21a99fbd773ec718707d9a85a587e3ddc08f7a801c53026d295be39"},"schema_version":"1.0","source":{"id":"1210.1941","kind":"arxiv","version":1}},"canonical_sha256":"ea6774d7abbd647d2edd880bc99172aed6a11ea8ab24c68933d696ae536a572e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea6774d7abbd647d2edd880bc99172aed6a11ea8ab24c68933d696ae536a572e","first_computed_at":"2026-05-18T03:08:04.413959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:04.413959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lxULJtHFSqLoZQEDiJ0HFDmteoE9cqp8SP+j57latkyDZCribvIH/DG3OChsZrNcsY5SkgsUf+GoeVeJD1guCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:04.414529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1941","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b758cd256c4659bbd4cbc5026e90bbef7974bb7475ff4e46ca7d526109ceefe","sha256:bc7066874233ca83150e99960605822206947d72ecdc1c4344e7e4cb42daac9b"],"state_sha256":"b4ba212432b2672cc28f36dd0dbef693b591c4e62f1652917d7e3d49e0f9f966"}