{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ECK6IILVQHRWYGWZVDQKVYWUQT","short_pith_number":"pith:ECK6IILV","schema_version":"1.0","canonical_sha256":"2095e4217581e36c1ad9a8e0aae2d484d1bfaa46bf877ce0126488dedd846d83","source":{"kind":"arxiv","id":"1812.10420","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Fathi Hassine","submitted_at":"2018-12-13T11:53:52Z","abstract_excerpt":"Let a fourth and a second order evolution equations be coupled via the interface by transmission conditions, and suppose that the first one is stabilized by a localized distributed feedback. What will then be the effect of such a partial stabilization on the decay of solutions at infinity? Is the behavior of the first component sufficient to stabilize the second one? The answer given in this paper is that sufficiently smooth solutions decay logarithmically at infinity even the feedback dissipation affects an arbitrarily small open subset of the interior. The method used, in this case, is based"},"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":"1812.10420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-13T11:53:52Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"0ed44c0736452101628801a43049e74aa64fa247fd33cb0b29c64daaff4c78a1","abstract_canon_sha256":"1e66b8a9bd6488554df5a9948c1c78042dead3209fe3c9d25bfdd93387af416c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:22.137881Z","signature_b64":"f3309CTM0KvnWigRCa9eHu8ys17L5k9vebWzqNTj8fuWXqls+U7CoVNRRTOZ/ayD8muxXp9xVnSnJ+q1EIj0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2095e4217581e36c1ad9a8e0aae2d484d1bfaa46bf877ce0126488dedd846d83","last_reissued_at":"2026-05-17T23:57:22.137160Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:22.137160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Fathi Hassine","submitted_at":"2018-12-13T11:53:52Z","abstract_excerpt":"Let a fourth and a second order evolution equations be coupled via the interface by transmission conditions, and suppose that the first one is stabilized by a localized distributed feedback. What will then be the effect of such a partial stabilization on the decay of solutions at infinity? Is the behavior of the first component sufficient to stabilize the second one? The answer given in this paper is that sufficiently smooth solutions decay logarithmically at infinity even the feedback dissipation affects an arbitrarily small open subset of the interior. The method used, in this case, is based"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10420","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":"1812.10420","created_at":"2026-05-17T23:57:22.137269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.10420v1","created_at":"2026-05-17T23:57:22.137269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10420","created_at":"2026-05-17T23:57:22.137269+00:00"},{"alias_kind":"pith_short_12","alias_value":"ECK6IILVQHRW","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"ECK6IILVQHRWYGWZ","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"ECK6IILV","created_at":"2026-05-18T12:32:22.470017+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/ECK6IILVQHRWYGWZVDQKVYWUQT","json":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT.json","graph_json":"https://pith.science/api/pith-number/ECK6IILVQHRWYGWZVDQKVYWUQT/graph.json","events_json":"https://pith.science/api/pith-number/ECK6IILVQHRWYGWZVDQKVYWUQT/events.json","paper":"https://pith.science/paper/ECK6IILV"},"agent_actions":{"view_html":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT","download_json":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT.json","view_paper":"https://pith.science/paper/ECK6IILV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.10420&json=true","fetch_graph":"https://pith.science/api/pith-number/ECK6IILVQHRWYGWZVDQKVYWUQT/graph.json","fetch_events":"https://pith.science/api/pith-number/ECK6IILVQHRWYGWZVDQKVYWUQT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT/action/storage_attestation","attest_author":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT/action/author_attestation","sign_citation":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT/action/citation_signature","submit_replication":"https://pith.science/pith/ECK6IILVQHRWYGWZVDQKVYWUQT/action/replication_record"}},"created_at":"2026-05-17T23:57:22.137269+00:00","updated_at":"2026-05-17T23:57:22.137269+00:00"}