{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:74NDFYE7H3OS5IXD7Q34N3YLZC","short_pith_number":"pith:74NDFYE7","schema_version":"1.0","canonical_sha256":"ff1a32e09f3edd2ea2e3fc37c6ef0bc8966258b1c093fe18072a66dd223ea2d1","source":{"kind":"arxiv","id":"1709.04406","version":1},"attestation_state":"computed","paper":{"title":"Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Masahiro Ikeda, Motohiro Sobajima","submitted_at":"2017-09-13T16:25:31Z","abstract_excerpt":"This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical time-dependent damping term (DW). The result is the sharp upper bound of lifespan of solution with respect to the small parameter $\\ep$ when $p_F(N)\\leq p\\leq p_0(N+\\mu)$, where $p_F(N)$ denotes the Fujita exponent for the nonlinear heat equations and $p_0(n)$ denotes the Strauss exponent for nonlinear wave equation in $n$-dimension with $\\mu=0$. Consequently, by connecting the result of D'Abbicco--Lucente--Reissig 2015, our result clarifies the threshold exponent $p_0(N+\\mu)$ "},"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":"1709.04406","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T16:25:31Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"77901559e99d1c313703109fffb159015214d049667101d90ab58492bc251a5e","abstract_canon_sha256":"fef23d9eba1270d52e1dc69ff5f8952cc2a47cc3641358099fc832e85ca51607"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:14.454440Z","signature_b64":"seCFsZ51YyZWm4k6qatz/Ji/m305ddc65TbrLDU5t9xuuwO0l9273KPkJ4Fqnnu99uNJ41vQP5XxxSZ/+u/qBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff1a32e09f3edd2ea2e3fc37c6ef0bc8966258b1c093fe18072a66dd223ea2d1","last_reissued_at":"2026-05-18T00:35:14.453945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:14.453945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Masahiro Ikeda, Motohiro Sobajima","submitted_at":"2017-09-13T16:25:31Z","abstract_excerpt":"This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical time-dependent damping term (DW). The result is the sharp upper bound of lifespan of solution with respect to the small parameter $\\ep$ when $p_F(N)\\leq p\\leq p_0(N+\\mu)$, where $p_F(N)$ denotes the Fujita exponent for the nonlinear heat equations and $p_0(n)$ denotes the Strauss exponent for nonlinear wave equation in $n$-dimension with $\\mu=0$. Consequently, by connecting the result of D'Abbicco--Lucente--Reissig 2015, our result clarifies the threshold exponent $p_0(N+\\mu)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04406","kind":"arxiv","version":1},"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":"1709.04406","created_at":"2026-05-18T00:35:14.454024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.04406v1","created_at":"2026-05-18T00:35:14.454024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04406","created_at":"2026-05-18T00:35:14.454024+00:00"},{"alias_kind":"pith_short_12","alias_value":"74NDFYE7H3OS","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"74NDFYE7H3OS5IXD","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"74NDFYE7","created_at":"2026-05-18T12:31:03.183658+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/74NDFYE7H3OS5IXD7Q34N3YLZC","json":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC.json","graph_json":"https://pith.science/api/pith-number/74NDFYE7H3OS5IXD7Q34N3YLZC/graph.json","events_json":"https://pith.science/api/pith-number/74NDFYE7H3OS5IXD7Q34N3YLZC/events.json","paper":"https://pith.science/paper/74NDFYE7"},"agent_actions":{"view_html":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC","download_json":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC.json","view_paper":"https://pith.science/paper/74NDFYE7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.04406&json=true","fetch_graph":"https://pith.science/api/pith-number/74NDFYE7H3OS5IXD7Q34N3YLZC/graph.json","fetch_events":"https://pith.science/api/pith-number/74NDFYE7H3OS5IXD7Q34N3YLZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC/action/storage_attestation","attest_author":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC/action/author_attestation","sign_citation":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC/action/citation_signature","submit_replication":"https://pith.science/pith/74NDFYE7H3OS5IXD7Q34N3YLZC/action/replication_record"}},"created_at":"2026-05-18T00:35:14.454024+00:00","updated_at":"2026-05-18T00:35:14.454024+00:00"}