{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GENNOFXUYHU3KTIA2F6AG3EC3K","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":"715c8f31ead7d97432ebf4959f001ad29b7f0a9cd16f49470d98138343fea3f6","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-23T14:23:38Z","title_canon_sha256":"d3331ea3941852a7babcf43fdeb1e8b0807b9fb6e9625934d19fe09f3e2f015a"},"schema_version":"1.0","source":{"id":"1606.07320","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07320","created_at":"2026-05-18T00:47:27Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07320v3","created_at":"2026-05-18T00:47:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07320","created_at":"2026-05-18T00:47:27Z"},{"alias_kind":"pith_short_12","alias_value":"GENNOFXUYHU3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GENNOFXUYHU3KTIA","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GENNOFXU","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:3e007937c498ad0e62d007024ad023b6a1de4882d4dcc8959dbf3f27bf13f509","target":"graph","created_at":"2026-05-18T00:47:27Z","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":"In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $\\partial_{t} u+ \\Delta^2 u=f(u),\\;t>0,\\;x\\in\\R^N,$ with $f(u)\\sim \\mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential nonlinearity $f$ such that $f(u)\\sim u^m$ as $u\\to 0,$ $m$ integer and $N(m-1)/4\\geq 2$, we show that the solution is global. Moreover, we obtain a decay estimates for large time for the nonlinear biharmonic heat equation as well as for the nonlinear heat equation. Our results extend to the nonlinear polyharmonic heat equation.","authors_text":"Mohamed Majdoub, Sarah Otsmane, Slim Tayachi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-23T14:23:38Z","title":"Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07320","kind":"arxiv","version":3},"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:cdd230e1e7e9d6fffeef53a84512968abec9f8f2a48c756f506b17d2a12904d2","target":"record","created_at":"2026-05-18T00:47:27Z","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":"715c8f31ead7d97432ebf4959f001ad29b7f0a9cd16f49470d98138343fea3f6","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-23T14:23:38Z","title_canon_sha256":"d3331ea3941852a7babcf43fdeb1e8b0807b9fb6e9625934d19fe09f3e2f015a"},"schema_version":"1.0","source":{"id":"1606.07320","kind":"arxiv","version":3}},"canonical_sha256":"311ad716f4c1e9b54d00d17c036c82da8403c392a7d3842c4e56d05d1ac20003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"311ad716f4c1e9b54d00d17c036c82da8403c392a7d3842c4e56d05d1ac20003","first_computed_at":"2026-05-18T00:47:27.086604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:27.086604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lJ/IAD5fpUROkvKyLHJxtJciGxbRxLxbX4NgE9CM9pLYT7EH09GaoGdkrk8FUjDmVxVpKPgzxW3EL5ydSRhMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:27.087127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07320","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd230e1e7e9d6fffeef53a84512968abec9f8f2a48c756f506b17d2a12904d2","sha256:3e007937c498ad0e62d007024ad023b6a1de4882d4dcc8959dbf3f27bf13f509"],"state_sha256":"210e843b17028ac94cda5dbe9b7cfa83230d1189a12bffcf379a77199db5467a"}