{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:U4JC7HZL6CO74M2UM67URA4ZYW","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":"9bbfada8cfd93c08e4dd298146c11cf14f6cb9ddeb7fcf0e888411301f34190f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-15T19:14:17Z","title_canon_sha256":"3527684ca5faa12cbb861d61590327818b158b1a42c501345d0d289edec4e795"},"schema_version":"1.0","source":{"id":"1406.3850","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3850","created_at":"2026-05-18T01:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3850v3","created_at":"2026-05-18T01:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3850","created_at":"2026-05-18T01:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"U4JC7HZL6CO7","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"U4JC7HZL6CO74M2U","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"U4JC7HZL","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:bc8adedd79188fb36a9c8262c7a67755e6c17fb0d43e02e71f94e0d5d67c8c5a","target":"graph","created_at":"2026-05-18T01:25:55Z","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 obtain a necessary and a sufficient condition expressed in terms of Wiener type tests involving the parabolic $W\\_{q'}^{2,1}$- capacity, where $q'=\\frac{q}{q-1}$, for the existence of large solutions to equation $\\prt\\_tu-\\Delta u+u^q=0$ in non-cylindrical domain, where $q\\textgreater{}1$. Also, we provide a sufficient condition associated with equation $\\prt\\_tu-\\Delta u+e^u-1=0$ . Besides, we apply our results to equation: $\\prt\\_tu-\\Delta u+a|\\nabla u|^p+bu^{q}=0$ for $a,b\\textgreater{}0$, $11$.","authors_text":"Laurent Veron (LMPT), Quoc-Hung Nguyen (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-15T19:14:17Z","title":"Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3850","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":"sha256:22d7d0cc9c20d449dc6cf07a6839288888d2de908fa174180285ab61768e4fba","target":"record","created_at":"2026-05-18T01:25:55Z","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":"9bbfada8cfd93c08e4dd298146c11cf14f6cb9ddeb7fcf0e888411301f34190f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-15T19:14:17Z","title_canon_sha256":"3527684ca5faa12cbb861d61590327818b158b1a42c501345d0d289edec4e795"},"schema_version":"1.0","source":{"id":"1406.3850","kind":"arxiv","version":3}},"canonical_sha256":"a7122f9f2bf09dfe335467bf488399c586888e21190bb519e4fbc4a288ce6319","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7122f9f2bf09dfe335467bf488399c586888e21190bb519e4fbc4a288ce6319","first_computed_at":"2026-05-18T01:25:55.806481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:55.806481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pjYcnhT4K7/NOcy+MwE6LfO8MCJG1kyvdRZjJXFVr5GrpHKH3PY+JkCgMrNdTq7L8kZbO46DMe2opjz+bo/AAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:55.807122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3850","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22d7d0cc9c20d449dc6cf07a6839288888d2de908fa174180285ab61768e4fba","sha256:bc8adedd79188fb36a9c8262c7a67755e6c17fb0d43e02e71f94e0d5d67c8c5a"],"state_sha256":"fdc97886b7f92c9fd54de1ef40b7205ccdbee8d1695ace149aac08ac65288eaa"}