{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YTBHUDJJYWUD5YKX4OY5KWEICO","short_pith_number":"pith:YTBHUDJJ","schema_version":"1.0","canonical_sha256":"c4c27a0d29c5a83ee157e3b1d558881384f9b1477b663c50904450658d9de104","source":{"kind":"arxiv","id":"1908.02961","version":1},"attestation_state":"computed","paper":{"title":"Global Estimates and Regularity of Retarded Parabolic Equations with Fast-growing Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Desheng Li","submitted_at":"2019-08-08T07:57:02Z","abstract_excerpt":"This paper is concerned with global estimates and regularity of solutions for the initial value problem of the retarded parabolic equation $$\\frac{\\patial u}{\\patial t}-\\Delta u=f(x,u)+g(u(x,t-r_1(t)),\\cdots,u(x,t-r_m(t)))+h(x,t)$$ in a bounded domain $\\Omega\\subset R^n$ with fast-growing nonlinearities and a dissipative structure, which is associated with the homogeneous Dirichlet boundary condition. Our results reveal some deeper inherent connections between dissipative structures and the regularity of solutions for such problems."},"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":"1908.02961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-08T07:57:02Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"85d16e673e45f8c8704de9f1554c68307d51ce699465a6bf5f8dcb882859bbb3","abstract_canon_sha256":"f76f8d4578a768f2a7ed2adfe24bff54f58c7cf2b0d6d05a8be219eafe66b0ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:25.289151Z","signature_b64":"StpBAO+NXlPjBiUCeD6R7lDO699i3C306ERG1zhHVI8ycx4K1lTYPuWMFj+et/Lk1GNTKyVrzHNjLCOgruKHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4c27a0d29c5a83ee157e3b1d558881384f9b1477b663c50904450658d9de104","last_reissued_at":"2026-07-04T23:52:25.288800Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:25.288800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Estimates and Regularity of Retarded Parabolic Equations with Fast-growing Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Desheng Li","submitted_at":"2019-08-08T07:57:02Z","abstract_excerpt":"This paper is concerned with global estimates and regularity of solutions for the initial value problem of the retarded parabolic equation $$\\frac{\\patial u}{\\patial t}-\\Delta u=f(x,u)+g(u(x,t-r_1(t)),\\cdots,u(x,t-r_m(t)))+h(x,t)$$ in a bounded domain $\\Omega\\subset R^n$ with fast-growing nonlinearities and a dissipative structure, which is associated with the homogeneous Dirichlet boundary condition. Our results reveal some deeper inherent connections between dissipative structures and the regularity of solutions for such problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02961","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02961/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.02961","created_at":"2026-07-04T23:52:25.288855+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02961v1","created_at":"2026-07-04T23:52:25.288855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02961","created_at":"2026-07-04T23:52:25.288855+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTBHUDJJYWUD","created_at":"2026-07-04T23:52:25.288855+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTBHUDJJYWUD5YKX","created_at":"2026-07-04T23:52:25.288855+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTBHUDJJ","created_at":"2026-07-04T23:52:25.288855+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/YTBHUDJJYWUD5YKX4OY5KWEICO","json":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO.json","graph_json":"https://pith.science/api/pith-number/YTBHUDJJYWUD5YKX4OY5KWEICO/graph.json","events_json":"https://pith.science/api/pith-number/YTBHUDJJYWUD5YKX4OY5KWEICO/events.json","paper":"https://pith.science/paper/YTBHUDJJ"},"agent_actions":{"view_html":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO","download_json":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO.json","view_paper":"https://pith.science/paper/YTBHUDJJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02961&json=true","fetch_graph":"https://pith.science/api/pith-number/YTBHUDJJYWUD5YKX4OY5KWEICO/graph.json","fetch_events":"https://pith.science/api/pith-number/YTBHUDJJYWUD5YKX4OY5KWEICO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO/action/storage_attestation","attest_author":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO/action/author_attestation","sign_citation":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO/action/citation_signature","submit_replication":"https://pith.science/pith/YTBHUDJJYWUD5YKX4OY5KWEICO/action/replication_record"}},"created_at":"2026-07-04T23:52:25.288855+00:00","updated_at":"2026-07-04T23:52:25.288855+00:00"}