{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CUEJEAY5KNV66LXNGGSNQZUHJG","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":"9923d5988be714b37c122e241b24753ed3f7f51de4ccb8904285ef8281a76d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-14T13:21:09Z","title_canon_sha256":"caf0b24ad706e11ddc1a2c5ddc5accd8c1b6b9ba88fd0496676b7d3631a59990"},"schema_version":"1.0","source":{"id":"1008.2443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2443","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2443v1","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2443","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"CUEJEAY5KNV6","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CUEJEAY5KNV66LXN","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CUEJEAY5","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:1d77a725e67fe415369f07f6fd5ce2b8ccef956285c9602ab4eca9207879ebcc","target":"graph","created_at":"2026-05-18T04:42:13Z","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":"We investigate the initial value problem for a semilinear heat equation with exponential-growth nonlinearity in two space dimension. First, we prove the local existence and unconditional uniqueness of solutions in the Sobolev space $H^1(\\R^2)$. The uniqueness part is non trivial although it follows Brezis-Cazenave's proof \\cite{Br} in the case of monomial nonlinearity in dimension $d\\geq3$. Next, %Following Caffarelli-Vasseur \\cite{cv}, we show that in the defocusing case our solution is bounded, and therefore exists for all time. In the focusing case, we prove that any solution with negative ","authors_text":"Mohamed Majdoub, Rym Jrad, Slim Ibrahim, Tarek Saanouni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-14T13:21:09Z","title":"Well posedness and unconditional non uniqueness for a 2D semilinear heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2443","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":"sha256:385eab01c61f29eea1dc24fa507a3a5c6fda311ab9ec67916446fa2c41e8b220","target":"record","created_at":"2026-05-18T04:42:13Z","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":"9923d5988be714b37c122e241b24753ed3f7f51de4ccb8904285ef8281a76d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-14T13:21:09Z","title_canon_sha256":"caf0b24ad706e11ddc1a2c5ddc5accd8c1b6b9ba88fd0496676b7d3631a59990"},"schema_version":"1.0","source":{"id":"1008.2443","kind":"arxiv","version":1}},"canonical_sha256":"150892031d536bef2eed31a4d8668749a2f7590d30f1714474245545190b87a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"150892031d536bef2eed31a4d8668749a2f7590d30f1714474245545190b87a3","first_computed_at":"2026-05-18T04:42:13.289196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:13.289196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"80PKlSn586aN9X4jDN1ThNGb2qxS98Pfn7qy1nXKAeTIt9/MatMhTWboKsL9/T7O02PdSJ3c9So30Y3B3fjzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:13.289865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:385eab01c61f29eea1dc24fa507a3a5c6fda311ab9ec67916446fa2c41e8b220","sha256:1d77a725e67fe415369f07f6fd5ce2b8ccef956285c9602ab4eca9207879ebcc"],"state_sha256":"a5c508f6048b6b33cba751dc57f2fead548f966ecfbe41613405e0329312a5cb"}