{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6OVWRTU7M3XJ4YAEYPPH4L7R6Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"10c5cfef4dcba86d396dca9c98e07e674aa61feda30d513ad89f1081144285f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-30T12:01:53Z","title_canon_sha256":"01d5c0673d5e6fa0829fa9e42e0e12382b2176fb590fa6709891e98123fc665f"},"schema_version":"1.0","source":{"id":"1203.6780","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6780","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6780v4","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6780","created_at":"2026-05-18T03:54:50Z"},{"alias_kind":"pith_short_12","alias_value":"6OVWRTU7M3XJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6OVWRTU7M3XJ4YAE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6OVWRTU7","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:7f7a8c2f9321cf5f1881c09d466c129c19de970338ebaf75da076b5f3ef223e5","target":"graph","created_at":"2026-05-18T03:54:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study the behavior of the energy of solutions of the wave equation with localized damping in exterior domain. We assume that the damper is positive at infinity. Under the Geometric Control Condition of Bardos et al (1992), we prove that: 1) The total energy decay like O(1/t) and L^2-norm is bounded for the solutions with initial data in (H_{0}^{1},L^{2}). 2) The total energy and the square of the L^2-norm, repectively, decay like O(1/t^{2}) and O(1/t) for a kind of the weighted initial data.","authors_text":"M. Daoulatli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-30T12:01:53Z","title":"Energy decay rates for solutions of the wave equation with linear damping in exterior domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6780","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8008e6b5a0ef9463d936f694477c7a6d0c94edd7a2ebe02a43dac30b91f84948","target":"record","created_at":"2026-05-18T03:54:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"10c5cfef4dcba86d396dca9c98e07e674aa61feda30d513ad89f1081144285f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-30T12:01:53Z","title_canon_sha256":"01d5c0673d5e6fa0829fa9e42e0e12382b2176fb590fa6709891e98123fc665f"},"schema_version":"1.0","source":{"id":"1203.6780","kind":"arxiv","version":4}},"canonical_sha256":"f3ab68ce9f66ee9e6004c3de7e2ff1f42a376b167503628648dfe2c3b5d61f05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3ab68ce9f66ee9e6004c3de7e2ff1f42a376b167503628648dfe2c3b5d61f05","first_computed_at":"2026-05-18T03:54:50.015040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:50.015040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"szo+s4+6PiCX0CkwBAh96g8tP7t9GnUKs1MtK+86x65VID/vTERa+XWyAe6N5vlt55kpDVJuQo3O6vqy7FB2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:50.015772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6780","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8008e6b5a0ef9463d936f694477c7a6d0c94edd7a2ebe02a43dac30b91f84948","sha256:7f7a8c2f9321cf5f1881c09d466c129c19de970338ebaf75da076b5f3ef223e5"],"state_sha256":"d8589f5848b46956033941f0f10f3d14c9bcf36e6a16343e976a90cdf9f50145"}