{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2KS5I4HGONRR67FSSNHA77IHK3","short_pith_number":"pith:2KS5I4HG","schema_version":"1.0","canonical_sha256":"d2a5d470e673631f7cb2934e0ffd0756cc616913f6439e3cc2a7fd41f4edeb03","source":{"kind":"arxiv","id":"1106.4232","version":1},"attestation_state":"computed","paper":{"title":"Approximate controllability for linear degenerate parabolic problems with bilinear control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"math.AP","authors_text":"Giuseppe Floridia, Piermarco Cannarsa","submitted_at":"2011-06-21T15:29:32Z","abstract_excerpt":"In this work we study the global approximate multiplicative controllability for the linear degenerate parabolic Cauchy-Neumann problem $$ \\{{array}{l} \\displaystyle{v_t-(a(x) v_x)_x =\\alpha (t,x)v\\,\\,\\qquad {in} \\qquad Q_T \\,=\\,(0,T)\\times(-1,1)} [2.5ex] \\displaystyle{a(x)v_x(t,x)|_{x=\\pm 1} = 0\\,\\,\\qquad\\qquad\\qquad\\,\\, t\\in (0,T)} [2.5ex] \\displaystyle{v(0,x)=v_0 (x) \\,\\qquad\\qquad\\qquad\\qquad\\quad\\,\\, x\\in (-1,1)}, {array}. $$ with the bilinear control $\\alpha(t,x)\\in L^\\infty (Q_T).$ The problem is strongly degenerate in the sense that $a\\in C^1([-1,1]),$ positive on $(-1,1),$ is allowed 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":"1106.4232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-21T15:29:32Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"efbe6ec476940a4b83ccadb0bddf2f7b7985d67f0b579ce4a461e79e0c4ba203","abstract_canon_sha256":"3e08a036a0eef1dd5b3ed4100ea27b03fd23fa37adf68dca9cc1736fa960ef93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:33.854207Z","signature_b64":"19ZAxL7r5uBh1x/WUlBmzCRjIuwIrL1x8rSRQYPoZOIIsq2Qsv3yjk1oCiEaTh5JANQ461iVowBa0wK1ZHWZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2a5d470e673631f7cb2934e0ffd0756cc616913f6439e3cc2a7fd41f4edeb03","last_reissued_at":"2026-05-18T04:19:33.853637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:33.853637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate controllability for linear degenerate parabolic problems with bilinear control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"math.AP","authors_text":"Giuseppe Floridia, Piermarco Cannarsa","submitted_at":"2011-06-21T15:29:32Z","abstract_excerpt":"In this work we study the global approximate multiplicative controllability for the linear degenerate parabolic Cauchy-Neumann problem $$ \\{{array}{l} \\displaystyle{v_t-(a(x) v_x)_x =\\alpha (t,x)v\\,\\,\\qquad {in} \\qquad Q_T \\,=\\,(0,T)\\times(-1,1)} [2.5ex] \\displaystyle{a(x)v_x(t,x)|_{x=\\pm 1} = 0\\,\\,\\qquad\\qquad\\qquad\\,\\, t\\in (0,T)} [2.5ex] \\displaystyle{v(0,x)=v_0 (x) \\,\\qquad\\qquad\\qquad\\qquad\\quad\\,\\, x\\in (-1,1)}, {array}. $$ with the bilinear control $\\alpha(t,x)\\in L^\\infty (Q_T).$ The problem is strongly degenerate in the sense that $a\\in C^1([-1,1]),$ positive on $(-1,1),$ is allowed t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4232","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":"1106.4232","created_at":"2026-05-18T04:19:33.853726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.4232v1","created_at":"2026-05-18T04:19:33.853726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4232","created_at":"2026-05-18T04:19:33.853726+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KS5I4HGONRR","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KS5I4HGONRR67FS","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KS5I4HG","created_at":"2026-05-18T12:26:18.847500+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/2KS5I4HGONRR67FSSNHA77IHK3","json":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3.json","graph_json":"https://pith.science/api/pith-number/2KS5I4HGONRR67FSSNHA77IHK3/graph.json","events_json":"https://pith.science/api/pith-number/2KS5I4HGONRR67FSSNHA77IHK3/events.json","paper":"https://pith.science/paper/2KS5I4HG"},"agent_actions":{"view_html":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3","download_json":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3.json","view_paper":"https://pith.science/paper/2KS5I4HG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.4232&json=true","fetch_graph":"https://pith.science/api/pith-number/2KS5I4HGONRR67FSSNHA77IHK3/graph.json","fetch_events":"https://pith.science/api/pith-number/2KS5I4HGONRR67FSSNHA77IHK3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3/action/storage_attestation","attest_author":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3/action/author_attestation","sign_citation":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3/action/citation_signature","submit_replication":"https://pith.science/pith/2KS5I4HGONRR67FSSNHA77IHK3/action/replication_record"}},"created_at":"2026-05-18T04:19:33.853726+00:00","updated_at":"2026-05-18T04:19:33.853726+00:00"}