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First we establish a Carleman estimate for this equation with overdetermining boundary data on a suitable lateral subboundary $\\Gamma \\times (-T,T)$. Second we apply the Carleman estimate to establish a both-sided estimate of $| u(\\cdot,0)|_{H^3(\\Omega)}$ by $\\"},"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":"1701.03052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-11T16:43:20Z","cross_cats_sorted":[],"title_canon_sha256":"1d063833c5204718df4ffffcb0deba0bbc56396920faea0702c57f0e36d0d562","abstract_canon_sha256":"7959d76125f516e92e3022a1709797ae508d57830737380731a41ed5bcff46b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:56.496229Z","signature_b64":"3IdiKgzeDUc2wOU9/jjsgXw0zIDbfCfRiGRPv6lyRMQMSA4/fdjRG2u79mm3ZHhvuYiy4CkXuk/PCo/Y/Zp4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84ffaa30383c1ccdc6b848b0487cd5fac90f75a90cca4f06f581fca55b2e0642","last_reissued_at":"2026-05-18T00:28:56.495726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:56.495726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Carleman estimate and application to an inverse source problem for a viscoelasticity model in anisotropic case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniela Sforza, Masahiro Yamamoto, Paola Loreti","submitted_at":"2017-01-11T16:43:20Z","abstract_excerpt":"We consider an anisotropic hyperbolic equation with memory term: $$ \\partial_t^2 u(x,t) = \\sum_{i,j=1}^n \\partial_i(a_{ij}(x)\\partial_ju) + \\int^t_0 \\sum_{| \\alpha| \\le 2} b_{\\alpha}(x,t,\\eta)\\partial_x^{\\alpha}u(x,\\eta) d\\eta + F(x,t) $$ for $x \\in \\Omega$ and $t\\in (0,T)$ or $\\in (-T,T)$, which is a model equation for viscoelasticity. First we establish a Carleman estimate for this equation with overdetermining boundary data on a suitable lateral subboundary $\\Gamma \\times (-T,T)$. Second we apply the Carleman estimate to establish a both-sided estimate of $| u(\\cdot,0)|_{H^3(\\Omega)}$ by $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03052","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":"1701.03052","created_at":"2026-05-18T00:28:56.495802+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.03052v1","created_at":"2026-05-18T00:28:56.495802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03052","created_at":"2026-05-18T00:28:56.495802+00:00"},{"alias_kind":"pith_short_12","alias_value":"QT72UMBYHQOM","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_16","alias_value":"QT72UMBYHQOM3RVY","created_at":"2026-05-18T12:31:39.905425+00:00"},{"alias_kind":"pith_short_8","alias_value":"QT72UMBY","created_at":"2026-05-18T12:31:39.905425+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/QT72UMBYHQOM3RVYJCYEQ7GV7L","json":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L.json","graph_json":"https://pith.science/api/pith-number/QT72UMBYHQOM3RVYJCYEQ7GV7L/graph.json","events_json":"https://pith.science/api/pith-number/QT72UMBYHQOM3RVYJCYEQ7GV7L/events.json","paper":"https://pith.science/paper/QT72UMBY"},"agent_actions":{"view_html":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L","download_json":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L.json","view_paper":"https://pith.science/paper/QT72UMBY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.03052&json=true","fetch_graph":"https://pith.science/api/pith-number/QT72UMBYHQOM3RVYJCYEQ7GV7L/graph.json","fetch_events":"https://pith.science/api/pith-number/QT72UMBYHQOM3RVYJCYEQ7GV7L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L/action/storage_attestation","attest_author":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L/action/author_attestation","sign_citation":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L/action/citation_signature","submit_replication":"https://pith.science/pith/QT72UMBYHQOM3RVYJCYEQ7GV7L/action/replication_record"}},"created_at":"2026-05-18T00:28:56.495802+00:00","updated_at":"2026-05-18T00:28:56.495802+00:00"}