{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:KSVI64O46QB3DXGXBFISRUDYK2","short_pith_number":"pith:KSVI64O4","schema_version":"1.0","canonical_sha256":"54aa8f71dcf403b1dcd7095128d078568732ef0cd7cab8ffd9262d143b4ee359","source":{"kind":"arxiv","id":"1209.5014","version":1},"attestation_state":"computed","paper":{"title":"Control and Stabilization of the Benjamin-Ono Equation on a Periodic Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares (IMPA), Lionel Rosier (IECN)","submitted_at":"2012-09-22T19:02:43Z","abstract_excerpt":"It was proved by Linares and Ortega that the linearized Benjamin-Ono equation posed on a periodic domain T with a distributed control supported on an arbitrary subdomain is exactly controllable and exponentially stabilizable. The aim of this paper is to extend those results to the full Benjamin-Ono equation. A feedback law in the form of a localized damping is incorporated in the equation. A smoothing effect established with the aid of a propagation of regularity property is used to prove the semi-global stabilization in L^2(T) of weak solutions obtained by the method of vanishing viscosity. T"},"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":"1209.5014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-22T19:02:43Z","cross_cats_sorted":[],"title_canon_sha256":"43a47b07aac1165485b20062fd97c9c20657af9e198820f6eb8bf7ca2275abc8","abstract_canon_sha256":"d8e3be491162a1d087e1606fd2f7de2eb5761c64ef7945457b3e3ff62f5c69ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:59.472760Z","signature_b64":"/9a6d14OJnBqmekxnOIy6WjM0huNU5yb/xs4WppHUt1v7FVChjT27xyOF9KWAvf9Swrf8301Lfo2WFp3vXgYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54aa8f71dcf403b1dcd7095128d078568732ef0cd7cab8ffd9262d143b4ee359","last_reissued_at":"2026-05-18T03:44:59.472013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:59.472013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Control and Stabilization of the Benjamin-Ono Equation on a Periodic Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares (IMPA), Lionel Rosier (IECN)","submitted_at":"2012-09-22T19:02:43Z","abstract_excerpt":"It was proved by Linares and Ortega that the linearized Benjamin-Ono equation posed on a periodic domain T with a distributed control supported on an arbitrary subdomain is exactly controllable and exponentially stabilizable. The aim of this paper is to extend those results to the full Benjamin-Ono equation. A feedback law in the form of a localized damping is incorporated in the equation. A smoothing effect established with the aid of a propagation of regularity property is used to prove the semi-global stabilization in L^2(T) of weak solutions obtained by the method of vanishing viscosity. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5014","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":"1209.5014","created_at":"2026-05-18T03:44:59.472151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.5014v1","created_at":"2026-05-18T03:44:59.472151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5014","created_at":"2026-05-18T03:44:59.472151+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSVI64O46QB3","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSVI64O46QB3DXGX","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSVI64O4","created_at":"2026-05-18T12:27:11.947152+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/KSVI64O46QB3DXGXBFISRUDYK2","json":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2.json","graph_json":"https://pith.science/api/pith-number/KSVI64O46QB3DXGXBFISRUDYK2/graph.json","events_json":"https://pith.science/api/pith-number/KSVI64O46QB3DXGXBFISRUDYK2/events.json","paper":"https://pith.science/paper/KSVI64O4"},"agent_actions":{"view_html":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2","download_json":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2.json","view_paper":"https://pith.science/paper/KSVI64O4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.5014&json=true","fetch_graph":"https://pith.science/api/pith-number/KSVI64O46QB3DXGXBFISRUDYK2/graph.json","fetch_events":"https://pith.science/api/pith-number/KSVI64O46QB3DXGXBFISRUDYK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2/action/storage_attestation","attest_author":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2/action/author_attestation","sign_citation":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2/action/citation_signature","submit_replication":"https://pith.science/pith/KSVI64O46QB3DXGXBFISRUDYK2/action/replication_record"}},"created_at":"2026-05-18T03:44:59.472151+00:00","updated_at":"2026-05-18T03:44:59.472151+00:00"}