{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IC44EZLVCCZCMB7BILLQYWJYNB","short_pith_number":"pith:IC44EZLV","schema_version":"1.0","canonical_sha256":"40b9c2657510b22607e142d70c59386869e3e98d9e854fc82945ef1e7ce1860d","source":{"kind":"arxiv","id":"1701.02191","version":1},"attestation_state":"computed","paper":{"title":"Actuator design for parabolic distributed parameter systems with the moment method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Emmanuel Tr\\'elat (LJLL, Enrique Zuazua, UPMC), Yannick Privat (LJLL)","submitted_at":"2017-01-09T14:28:00Z","abstract_excerpt":"In this paper, we model and solve the problem of designing in an optimal way actuators for parabolic partial differential equations settled on a bounded open connected subset $\\Omega$ of IR n. We optimize not only the location but also the shape of actuators, by finding what is the optimal distribution of actuators in $\\Omega$, over all possible such distributions of a given measure. Using the moment method, we formulate a spectral optimal design problem, which consists of maximizing a criterion corresponding to an average over random initial data of the largest L 2-energy of controllers. Sinc"},"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":"1701.02191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-09T14:28:00Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"551bae49813d5e1dedfb1ed6f5a4f4e8084cada535b0da9c244cae42a639ee8a","abstract_canon_sha256":"f19d7d9e35e2d229b56bc0b747ff672cb187f1d66209107926379ad0f8a9d8da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:11.474449Z","signature_b64":"LohRrE9KuMeyj+uLLF/0t19YRBUg+9jAYesnQ7JAp6IhJhK6XZz0ZOqV/0U5xm75TOTUrN+39IdwwB3tJ8r5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40b9c2657510b22607e142d70c59386869e3e98d9e854fc82945ef1e7ce1860d","last_reissued_at":"2026-05-18T00:53:11.474001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:11.474001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Actuator design for parabolic distributed parameter systems with the moment method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Emmanuel Tr\\'elat (LJLL, Enrique Zuazua, UPMC), Yannick Privat (LJLL)","submitted_at":"2017-01-09T14:28:00Z","abstract_excerpt":"In this paper, we model and solve the problem of designing in an optimal way actuators for parabolic partial differential equations settled on a bounded open connected subset $\\Omega$ of IR n. We optimize not only the location but also the shape of actuators, by finding what is the optimal distribution of actuators in $\\Omega$, over all possible such distributions of a given measure. Using the moment method, we formulate a spectral optimal design problem, which consists of maximizing a criterion corresponding to an average over random initial data of the largest L 2-energy of controllers. Sinc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02191","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":"1701.02191","created_at":"2026-05-18T00:53:11.474060+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02191v1","created_at":"2026-05-18T00:53:11.474060+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02191","created_at":"2026-05-18T00:53:11.474060+00:00"},{"alias_kind":"pith_short_12","alias_value":"IC44EZLVCCZC","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IC44EZLVCCZCMB7B","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IC44EZLV","created_at":"2026-05-18T12:31:21.493067+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/IC44EZLVCCZCMB7BILLQYWJYNB","json":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB.json","graph_json":"https://pith.science/api/pith-number/IC44EZLVCCZCMB7BILLQYWJYNB/graph.json","events_json":"https://pith.science/api/pith-number/IC44EZLVCCZCMB7BILLQYWJYNB/events.json","paper":"https://pith.science/paper/IC44EZLV"},"agent_actions":{"view_html":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB","download_json":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB.json","view_paper":"https://pith.science/paper/IC44EZLV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02191&json=true","fetch_graph":"https://pith.science/api/pith-number/IC44EZLVCCZCMB7BILLQYWJYNB/graph.json","fetch_events":"https://pith.science/api/pith-number/IC44EZLVCCZCMB7BILLQYWJYNB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB/action/storage_attestation","attest_author":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB/action/author_attestation","sign_citation":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB/action/citation_signature","submit_replication":"https://pith.science/pith/IC44EZLVCCZCMB7BILLQYWJYNB/action/replication_record"}},"created_at":"2026-05-18T00:53:11.474060+00:00","updated_at":"2026-05-18T00:53:11.474060+00:00"}