{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ITUMWWKUCXDITXE5GFIG3MWCWG","short_pith_number":"pith:ITUMWWKU","schema_version":"1.0","canonical_sha256":"44e8cb595415c689dc9d31506db2c2b1887fdaa1eaed20f690937c1f6fbdc6b6","source":{"kind":"arxiv","id":"1810.10232","version":2},"attestation_state":"computed","paper":{"title":"Global existence and lifespan for semilinear wave equations with mixed nonlinear terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengbo Wang, Daoyuan Fang, Wei Dai","submitted_at":"2018-10-24T07:57:58Z","abstract_excerpt":"Firstly, we study the equation $\\square u = |u|^{q_c}+ |\\partial u|^p$ with small data, where $q_c$ is the critical power of Strauss conjecture and $p\\geq q_c.$ We obtain the optimal lifespan $\\ln({T_\\varepsilon})\\approx\\varepsilon^{-q_c(q_c-1)}$ in $n=3$, and improve the lower-bound of $T_\\varepsilon$ from $\\exp({c\\varepsilon^{-(q_c-1)}})$ to $\\exp({c\\varepsilon^{-(q_c-1)^2/2}})$ in $n=2$. Then, we study the Cauchy problem with small initial data for a system of semilinear wave equations $\\square u = |v|^q,$ $ \\square v = |\\partial_t u|^p$ in 3-dimensional space with $q<2$. We obtain that thi"},"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":"1810.10232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-24T07:57:58Z","cross_cats_sorted":[],"title_canon_sha256":"5499c8a8035314d36ce896cf372118da192a114b3af544c6ec269141059a5091","abstract_canon_sha256":"54227016fb6560ef7921216942d24cf5e1a5fe00c01ab012c9d12ea6f3774c00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:50.865462Z","signature_b64":"lNkE3W7l5wcayE2yaU+1duqG3NbiLEyhwdo4jkdDphAzIgl77hezQzktbw38hwfw6trippYiefkKhApL8UOTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44e8cb595415c689dc9d31506db2c2b1887fdaa1eaed20f690937c1f6fbdc6b6","last_reissued_at":"2026-05-17T23:47:50.864738Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:50.864738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global existence and lifespan for semilinear wave equations with mixed nonlinear terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengbo Wang, Daoyuan Fang, Wei Dai","submitted_at":"2018-10-24T07:57:58Z","abstract_excerpt":"Firstly, we study the equation $\\square u = |u|^{q_c}+ |\\partial u|^p$ with small data, where $q_c$ is the critical power of Strauss conjecture and $p\\geq q_c.$ We obtain the optimal lifespan $\\ln({T_\\varepsilon})\\approx\\varepsilon^{-q_c(q_c-1)}$ in $n=3$, and improve the lower-bound of $T_\\varepsilon$ from $\\exp({c\\varepsilon^{-(q_c-1)}})$ to $\\exp({c\\varepsilon^{-(q_c-1)^2/2}})$ in $n=2$. Then, we study the Cauchy problem with small initial data for a system of semilinear wave equations $\\square u = |v|^q,$ $ \\square v = |\\partial_t u|^p$ in 3-dimensional space with $q<2$. We obtain that thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10232","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":"1810.10232","created_at":"2026-05-17T23:47:50.864855+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10232v2","created_at":"2026-05-17T23:47:50.864855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10232","created_at":"2026-05-17T23:47:50.864855+00:00"},{"alias_kind":"pith_short_12","alias_value":"ITUMWWKUCXDI","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"ITUMWWKUCXDITXE5","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"ITUMWWKU","created_at":"2026-05-18T12:32:31.084164+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/ITUMWWKUCXDITXE5GFIG3MWCWG","json":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG.json","graph_json":"https://pith.science/api/pith-number/ITUMWWKUCXDITXE5GFIG3MWCWG/graph.json","events_json":"https://pith.science/api/pith-number/ITUMWWKUCXDITXE5GFIG3MWCWG/events.json","paper":"https://pith.science/paper/ITUMWWKU"},"agent_actions":{"view_html":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG","download_json":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG.json","view_paper":"https://pith.science/paper/ITUMWWKU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10232&json=true","fetch_graph":"https://pith.science/api/pith-number/ITUMWWKUCXDITXE5GFIG3MWCWG/graph.json","fetch_events":"https://pith.science/api/pith-number/ITUMWWKUCXDITXE5GFIG3MWCWG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG/action/storage_attestation","attest_author":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG/action/author_attestation","sign_citation":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG/action/citation_signature","submit_replication":"https://pith.science/pith/ITUMWWKUCXDITXE5GFIG3MWCWG/action/replication_record"}},"created_at":"2026-05-17T23:47:50.864855+00:00","updated_at":"2026-05-17T23:47:50.864855+00:00"}