{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NVDSAPEICCGXZOTJB3CONRWV7E","short_pith_number":"pith:NVDSAPEI","canonical_record":{"source":{"id":"1104.3279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-17T06:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"a35c1b44769339a03979ff66698970c9a31677eb575ee0a18d01cb695ef77355","abstract_canon_sha256":"ba35c36e0bb54bebfd5ba18d8f8f5d0ec12871f469119bf893022ec116f5d194"},"schema_version":"1.0"},"canonical_sha256":"6d47203c88108d7cba690ec4e6c6d5f9396ff32df95d96a187241405d7037143","source":{"kind":"arxiv","id":"1104.3279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3279","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3279v2","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3279","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"NVDSAPEICCGX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NVDSAPEICCGXZOTJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NVDSAPEI","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NVDSAPEICCGXZOTJB3CONRWV7E","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-17T06:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"a35c1b44769339a03979ff66698970c9a31677eb575ee0a18d01cb695ef77355","abstract_canon_sha256":"ba35c36e0bb54bebfd5ba18d8f8f5d0ec12871f469119bf893022ec116f5d194"},"schema_version":"1.0"},"canonical_sha256":"6d47203c88108d7cba690ec4e6c6d5f9396ff32df95d96a187241405d7037143","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:33.964293Z","signature_b64":"fRGHwE/KtufAnvZuUHdnSeqcDhHcsCmyUtTqjTTOZT4sfVrbh5qIgMV32WmMWHwNiI/5/osP75JWdCYBm7xGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d47203c88108d7cba690ec4e6c6d5f9396ff32df95d96a187241405d7037143","last_reissued_at":"2026-05-18T04:23:33.963832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:33.963832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3279","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sn2Yo7JceYJQEsYmYoQ4T5ZOPK98XlGdoS+BAFRX3JgP/PDOelLWXHXA+5wTE0wautAGVY4NyM6ah/3ihCUyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:01:04.527159Z"},"content_sha256":"1aef6e5bb063eff0689bd642b90a809208fae22d9f5f470445be483973fd611b","schema_version":"1.0","event_id":"sha256:1aef6e5bb063eff0689bd642b90a809208fae22d9f5f470445be483973fd611b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NVDSAPEICCGXZOTJB3CONRWV7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Wave Equations with Nonlinear Damping and Source Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boling Guo, Fei Liang, Hongjun Gao","submitted_at":"2011-04-17T06:00:58Z","abstract_excerpt":"In this paper, we discuss an initial boundary value problem for the stochastic wave equation involving the nonlinear damping term $|u_t|^{q-2}u_t$ and a source term of the type $|u|^{p-2}u$. We firstly establish the local existence and uniqueness of solution by the Galerkin approximation method and show that the solution is global for $q\\geq p$. Secondly, by an appropriate energy inequality, the local solution of the stochastic equations will blow up with positive probability or explosive in energy sense for $p>q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3279","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"edPXiWueJu5v4JUgpUzYoZc3jyFBdhW5kKdgS9SufNT65hZcFMS7hHNxS50tTXDX5R/ZpowYu3mOrSJ05TLKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:01:04.527515Z"},"content_sha256":"275c6d37379cff9dbc8e7a20a316fbb11d55054e29dc0a1cc64f306fd7bb9a7e","schema_version":"1.0","event_id":"sha256:275c6d37379cff9dbc8e7a20a316fbb11d55054e29dc0a1cc64f306fd7bb9a7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/bundle.json","state_url":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVDSAPEICCGXZOTJB3CONRWV7E/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T18:01:04Z","links":{"resolver":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E","bundle":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/bundle.json","state":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVDSAPEICCGXZOTJB3CONRWV7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NVDSAPEICCGXZOTJB3CONRWV7E","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":"ba35c36e0bb54bebfd5ba18d8f8f5d0ec12871f469119bf893022ec116f5d194","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-17T06:00:58Z","title_canon_sha256":"a35c1b44769339a03979ff66698970c9a31677eb575ee0a18d01cb695ef77355"},"schema_version":"1.0","source":{"id":"1104.3279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3279","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3279v2","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3279","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"NVDSAPEICCGX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NVDSAPEICCGXZOTJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NVDSAPEI","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:275c6d37379cff9dbc8e7a20a316fbb11d55054e29dc0a1cc64f306fd7bb9a7e","target":"graph","created_at":"2026-05-18T04:23:33Z","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 discuss an initial boundary value problem for the stochastic wave equation involving the nonlinear damping term $|u_t|^{q-2}u_t$ and a source term of the type $|u|^{p-2}u$. We firstly establish the local existence and uniqueness of solution by the Galerkin approximation method and show that the solution is global for $q\\geq p$. Secondly, by an appropriate energy inequality, the local solution of the stochastic equations will blow up with positive probability or explosive in energy sense for $p>q$.","authors_text":"Boling Guo, Fei Liang, Hongjun Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-17T06:00:58Z","title":"Stochastic Wave Equations with Nonlinear Damping and Source Terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3279","kind":"arxiv","version":2},"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":"sha256:1aef6e5bb063eff0689bd642b90a809208fae22d9f5f470445be483973fd611b","target":"record","created_at":"2026-05-18T04:23:33Z","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":"ba35c36e0bb54bebfd5ba18d8f8f5d0ec12871f469119bf893022ec116f5d194","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-17T06:00:58Z","title_canon_sha256":"a35c1b44769339a03979ff66698970c9a31677eb575ee0a18d01cb695ef77355"},"schema_version":"1.0","source":{"id":"1104.3279","kind":"arxiv","version":2}},"canonical_sha256":"6d47203c88108d7cba690ec4e6c6d5f9396ff32df95d96a187241405d7037143","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d47203c88108d7cba690ec4e6c6d5f9396ff32df95d96a187241405d7037143","first_computed_at":"2026-05-18T04:23:33.963832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:33.963832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fRGHwE/KtufAnvZuUHdnSeqcDhHcsCmyUtTqjTTOZT4sfVrbh5qIgMV32WmMWHwNiI/5/osP75JWdCYBm7xGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:33.964293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1aef6e5bb063eff0689bd642b90a809208fae22d9f5f470445be483973fd611b","sha256:275c6d37379cff9dbc8e7a20a316fbb11d55054e29dc0a1cc64f306fd7bb9a7e"],"state_sha256":"7af8550534268e1e259bd36be01b0b0053a4bab2b7e2c06a2f439b663171d121"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"drWnI+qU7FCCcK1LnM7RAeRAE7aJr7+hwqT7oOqkJk2aHk0PMFxKe4TvSCXM+OQvhezwLyAyiuc82nVcyRXUCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:01:04.529307Z","bundle_sha256":"86d6fdec8497b5be71dced6292ba323969b8397de37a36cc280eca284a1bb8dd"}}