{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CEUMWJBV5UCJ2FA5AYEUZXN5GZ","short_pith_number":"pith:CEUMWJBV","schema_version":"1.0","canonical_sha256":"1128cb2435ed049d141d06094cddbd364c32ce160876fbe4939baf6b12ffb24f","source":{"kind":"arxiv","id":"1110.1837","version":1},"attestation_state":"computed","paper":{"title":"Global attractor and stabilization for a coupled PDE-ODE system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Messoud Efendiev, Sergey Zelik","submitted_at":"2011-10-09T13:40:28Z","abstract_excerpt":"We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem.\n  In the case where the ODE-component of the system is monotone, we establish the existence of a smooth global attractor of finite Hausdorff and fractal dimension.\n  The case of the non-monotone ODE-component is much more complicated. In particular, the set of equilibria becomes non-compact here and contains a huge number of essentially discontinuous solutions. Nevertheless, we prove the stabilization of any trajectory to a single equ"},"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":"1110.1837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-09T13:40:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6f63c294fae5a2f3c75f1e66f3b83cff4624b43bff803dd783d2bacdfd28bd8e","abstract_canon_sha256":"e0254dd589c598611fbe66012ab9849a5bf3ba435b217bd4fc56cca86bcdb80d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:19.561924Z","signature_b64":"Vz4JnTYYvgdZp1VV4MqtKDyb3gh7SyKGMm1+HE0cAbA/gdMaWn2BEJsiq42QgDvwS3BrMCQEmN0N/K1cR7edAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1128cb2435ed049d141d06094cddbd364c32ce160876fbe4939baf6b12ffb24f","last_reissued_at":"2026-05-18T04:11:19.561473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:19.561473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global attractor and stabilization for a coupled PDE-ODE system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Messoud Efendiev, Sergey Zelik","submitted_at":"2011-10-09T13:40:28Z","abstract_excerpt":"We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem.\n  In the case where the ODE-component of the system is monotone, we establish the existence of a smooth global attractor of finite Hausdorff and fractal dimension.\n  The case of the non-monotone ODE-component is much more complicated. In particular, the set of equilibria becomes non-compact here and contains a huge number of essentially discontinuous solutions. Nevertheless, we prove the stabilization of any trajectory to a single equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1837","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":"1110.1837","created_at":"2026-05-18T04:11:19.561530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1837v1","created_at":"2026-05-18T04:11:19.561530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1837","created_at":"2026-05-18T04:11:19.561530+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEUMWJBV5UCJ","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEUMWJBV5UCJ2FA5","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEUMWJBV","created_at":"2026-05-18T12:26:26.731475+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/CEUMWJBV5UCJ2FA5AYEUZXN5GZ","json":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ.json","graph_json":"https://pith.science/api/pith-number/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/graph.json","events_json":"https://pith.science/api/pith-number/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/events.json","paper":"https://pith.science/paper/CEUMWJBV"},"agent_actions":{"view_html":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ","download_json":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ.json","view_paper":"https://pith.science/paper/CEUMWJBV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1837&json=true","fetch_graph":"https://pith.science/api/pith-number/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/action/storage_attestation","attest_author":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/action/author_attestation","sign_citation":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/action/citation_signature","submit_replication":"https://pith.science/pith/CEUMWJBV5UCJ2FA5AYEUZXN5GZ/action/replication_record"}},"created_at":"2026-05-18T04:11:19.561530+00:00","updated_at":"2026-05-18T04:11:19.561530+00:00"}