{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V35R4NQ6K6KTNP5EZ24RNTD63Q","short_pith_number":"pith:V35R4NQ6","schema_version":"1.0","canonical_sha256":"aefb1e361e579536bfa4ceb916cc7edc0086572235e9705894b156aefddd2728","source":{"kind":"arxiv","id":"1807.05005","version":2},"attestation_state":"computed","paper":{"title":"Observability inequalities for transport equations through Carleman estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Giuseppe Floridia, Masahiro Yamamoto, Piermarco Cannarsa","submitted_at":"2018-07-13T11:06:00Z","abstract_excerpt":"We consider the transport equation $\\ppp_t u(x,t) + H(t)\\cdot \\nabla u(x,t) = 0$ in $\\OOO\\times(0,T),$ where $T>0$ and $\\OOO\\subset \\R^d $ is a bounded domain with smooth boundary $\\ppp\\OOO$. First, we prove a Carleman estimate for solutions of finite energy with piecewise continuous weight functions. Then, under a further condition which guarantees that the orbits of $H$ intersect $\\ppp\\OOO$, we prove an energy estimate which in turn yields an observability inequality. Our results are motivated by applications to inverse 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":"1807.05005","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-13T11:06:00Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"52047919929e2083bb5971bab345bb5406af307bf5704c8a82a55c6469f68fad","abstract_canon_sha256":"c2279daa854bed6eee9ecadba3768152d89ad75a3d68d91491f3d333eb338dfc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:52.699865Z","signature_b64":"gR4KUIfVx6UpChwo79BQBOlE3Z/VZoPCACB08TwV/8CiR5zf280RMxcY4Qi7vnpGpRNs2/Jhl0b0UkdHgh5fDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aefb1e361e579536bfa4ceb916cc7edc0086572235e9705894b156aefddd2728","last_reissued_at":"2026-05-17T23:52:52.699155Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:52.699155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Observability inequalities for transport equations through Carleman estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Giuseppe Floridia, Masahiro Yamamoto, Piermarco Cannarsa","submitted_at":"2018-07-13T11:06:00Z","abstract_excerpt":"We consider the transport equation $\\ppp_t u(x,t) + H(t)\\cdot \\nabla u(x,t) = 0$ in $\\OOO\\times(0,T),$ where $T>0$ and $\\OOO\\subset \\R^d $ is a bounded domain with smooth boundary $\\ppp\\OOO$. First, we prove a Carleman estimate for solutions of finite energy with piecewise continuous weight functions. Then, under a further condition which guarantees that the orbits of $H$ intersect $\\ppp\\OOO$, we prove an energy estimate which in turn yields an observability inequality. Our results are motivated by applications to inverse problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05005","kind":"arxiv","version":2},"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":"1807.05005","created_at":"2026-05-17T23:52:52.699275+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.05005v2","created_at":"2026-05-17T23:52:52.699275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05005","created_at":"2026-05-17T23:52:52.699275+00:00"},{"alias_kind":"pith_short_12","alias_value":"V35R4NQ6K6KT","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"V35R4NQ6K6KTNP5E","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"V35R4NQ6","created_at":"2026-05-18T12:32:56.356000+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/V35R4NQ6K6KTNP5EZ24RNTD63Q","json":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q.json","graph_json":"https://pith.science/api/pith-number/V35R4NQ6K6KTNP5EZ24RNTD63Q/graph.json","events_json":"https://pith.science/api/pith-number/V35R4NQ6K6KTNP5EZ24RNTD63Q/events.json","paper":"https://pith.science/paper/V35R4NQ6"},"agent_actions":{"view_html":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q","download_json":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q.json","view_paper":"https://pith.science/paper/V35R4NQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.05005&json=true","fetch_graph":"https://pith.science/api/pith-number/V35R4NQ6K6KTNP5EZ24RNTD63Q/graph.json","fetch_events":"https://pith.science/api/pith-number/V35R4NQ6K6KTNP5EZ24RNTD63Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q/action/storage_attestation","attest_author":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q/action/author_attestation","sign_citation":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q/action/citation_signature","submit_replication":"https://pith.science/pith/V35R4NQ6K6KTNP5EZ24RNTD63Q/action/replication_record"}},"created_at":"2026-05-17T23:52:52.699275+00:00","updated_at":"2026-05-17T23:52:52.699275+00:00"}