{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XBQDMJLDCSQRY2IB3P5MAX25J6","short_pith_number":"pith:XBQDMJLD","schema_version":"1.0","canonical_sha256":"b86036256314a11c6901dbfac05f5d4f95f6c9aa2b3319ab279eb118bb2fa65f","source":{"kind":"arxiv","id":"1804.09947","version":1},"attestation_state":"computed","paper":{"title":"Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.AP","authors_text":"Anton Savostianov, Shane Cooper","submitted_at":"2018-04-26T08:57:51Z","abstract_excerpt":"Homogenisation of global $\\mathcal{A}^\\epsilon$ and exponential $\\mathcal{M}^\\epsilon$ attractors for the damped semi-linear anisotropic wave equation $\\partial_t^2 u^\\epsilon +\\gamma\\partial_t u^\\epsilon-{\\rm div} \\left(a\\left( \\tfrac{x}{\\epsilon} \\right)\\nabla u^\\epsilon \\right)+f(u^\\epsilon)=g$, on a bounded domain $\\Omega \\subset \\mathbb{R}^3$, is performed. Order-sharp estimates between trajectories $u^\\epsilon(t)$ and their homogenised trajectories $u^0(t)$ are established. These estimates are given in terms of the operator-norm difference between resolvents of the elliptic operator ${\\r"},"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":"1804.09947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-26T08:57:51Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"c1ce38aa520b012639b60df0a9d95596ec7fa71bd129fb050851bb507a906764","abstract_canon_sha256":"95099f9f371f37e610c7ae4b31f1a01c61f6b68c53181f019e17ff8e59a91e8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:25.645773Z","signature_b64":"U2MILteYCGDiXI7snPUA5j5FPoH9gceOuRMcg1WeiqEOfTYsif/J0WfZpoyWl28hYWxGCQ6vWerVPQm0S5FHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b86036256314a11c6901dbfac05f5d4f95f6c9aa2b3319ab279eb118bb2fa65f","last_reissued_at":"2026-05-18T00:17:25.645095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:25.645095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.AP","authors_text":"Anton Savostianov, Shane Cooper","submitted_at":"2018-04-26T08:57:51Z","abstract_excerpt":"Homogenisation of global $\\mathcal{A}^\\epsilon$ and exponential $\\mathcal{M}^\\epsilon$ attractors for the damped semi-linear anisotropic wave equation $\\partial_t^2 u^\\epsilon +\\gamma\\partial_t u^\\epsilon-{\\rm div} \\left(a\\left( \\tfrac{x}{\\epsilon} \\right)\\nabla u^\\epsilon \\right)+f(u^\\epsilon)=g$, on a bounded domain $\\Omega \\subset \\mathbb{R}^3$, is performed. Order-sharp estimates between trajectories $u^\\epsilon(t)$ and their homogenised trajectories $u^0(t)$ are established. These estimates are given in terms of the operator-norm difference between resolvents of the elliptic operator ${\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09947","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":"1804.09947","created_at":"2026-05-18T00:17:25.645197+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.09947v1","created_at":"2026-05-18T00:17:25.645197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09947","created_at":"2026-05-18T00:17:25.645197+00:00"},{"alias_kind":"pith_short_12","alias_value":"XBQDMJLDCSQR","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XBQDMJLDCSQRY2IB","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XBQDMJLD","created_at":"2026-05-18T12:33:01.666342+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/XBQDMJLDCSQRY2IB3P5MAX25J6","json":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6.json","graph_json":"https://pith.science/api/pith-number/XBQDMJLDCSQRY2IB3P5MAX25J6/graph.json","events_json":"https://pith.science/api/pith-number/XBQDMJLDCSQRY2IB3P5MAX25J6/events.json","paper":"https://pith.science/paper/XBQDMJLD"},"agent_actions":{"view_html":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6","download_json":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6.json","view_paper":"https://pith.science/paper/XBQDMJLD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.09947&json=true","fetch_graph":"https://pith.science/api/pith-number/XBQDMJLDCSQRY2IB3P5MAX25J6/graph.json","fetch_events":"https://pith.science/api/pith-number/XBQDMJLDCSQRY2IB3P5MAX25J6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6/action/storage_attestation","attest_author":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6/action/author_attestation","sign_citation":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6/action/citation_signature","submit_replication":"https://pith.science/pith/XBQDMJLDCSQRY2IB3P5MAX25J6/action/replication_record"}},"created_at":"2026-05-18T00:17:25.645197+00:00","updated_at":"2026-05-18T00:17:25.645197+00:00"}