{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NVDSAPEICCGXZOTJB3CONRWV7E","short_pith_number":"pith:NVDSAPEI","schema_version":"1.0","canonical_sha256":"6d47203c88108d7cba690ec4e6c6d5f9396ff32df95d96a187241405d7037143","source":{"kind":"arxiv","id":"1104.3279","version":2},"attestation_state":"computed","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 $p>q$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.3279","created_at":"2026-05-18T04:23:33.963902+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.3279v2","created_at":"2026-05-18T04:23:33.963902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3279","created_at":"2026-05-18T04:23:33.963902+00:00"},{"alias_kind":"pith_short_12","alias_value":"NVDSAPEICCGX","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NVDSAPEICCGXZOTJ","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NVDSAPEI","created_at":"2026-05-18T12:26:37.096874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E","json":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E.json","graph_json":"https://pith.science/api/pith-number/NVDSAPEICCGXZOTJB3CONRWV7E/graph.json","events_json":"https://pith.science/api/pith-number/NVDSAPEICCGXZOTJB3CONRWV7E/events.json","paper":"https://pith.science/paper/NVDSAPEI"},"agent_actions":{"view_html":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E","download_json":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E.json","view_paper":"https://pith.science/paper/NVDSAPEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.3279&json=true","fetch_graph":"https://pith.science/api/pith-number/NVDSAPEICCGXZOTJB3CONRWV7E/graph.json","fetch_events":"https://pith.science/api/pith-number/NVDSAPEICCGXZOTJB3CONRWV7E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/action/storage_attestation","attest_author":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/action/author_attestation","sign_citation":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/action/citation_signature","submit_replication":"https://pith.science/pith/NVDSAPEICCGXZOTJB3CONRWV7E/action/replication_record"}},"created_at":"2026-05-18T04:23:33.963902+00:00","updated_at":"2026-05-18T04:23:33.963902+00:00"}