{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WNNP3CMVR2HAPCKK7Q2L75CLJY","short_pith_number":"pith:WNNP3CMV","schema_version":"1.0","canonical_sha256":"b35afd89958e8e07894afc34bff44b4e0ddaae85e06ec67d3a5a45259695e198","source":{"kind":"arxiv","id":"1511.04592","version":1},"attestation_state":"computed","paper":{"title":"Infinite energy solutions for critical wave equation with fractional damping in unbounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anton Savostianov","submitted_at":"2015-11-14T18:24:01Z","abstract_excerpt":"This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\\mathbb{R}^3$ with fractional damping of the form $(-\\Delta_x+1)^\\frac{1}{2}\\partial_t u$. The work extends previously known results for bounded domains in finite energy case. Furthermore, well-posedness and existence of locally-compact smooth attractors for the critical quintic non-linearity are obtained under less restrictive assumptions on non-linearity, relaxing some artificial technical conditions used before. This is achieved by virtue of new type Lyapunov functional that allow"},"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":"1511.04592","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-14T18:24:01Z","cross_cats_sorted":[],"title_canon_sha256":"113625e428c791b8e5b66ca3a9533b7b26ad693c7b966955cd29da29bd0df06b","abstract_canon_sha256":"6b3547634bf9c2e4e746ff43eea9a33639b6e7d498bdb0ed43ba12dc26dd241d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:52.246097Z","signature_b64":"OCt9ymH3BPP5/J3cNwx44pRRVle9jzn/MJvLxLT0D/NpEZOMb2uPPy38EiDZ/Lx4sRsEFMK8V03PKIAxQuPHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b35afd89958e8e07894afc34bff44b4e0ddaae85e06ec67d3a5a45259695e198","last_reissued_at":"2026-05-18T01:26:52.245519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:52.245519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite energy solutions for critical wave equation with fractional damping in unbounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anton Savostianov","submitted_at":"2015-11-14T18:24:01Z","abstract_excerpt":"This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\\mathbb{R}^3$ with fractional damping of the form $(-\\Delta_x+1)^\\frac{1}{2}\\partial_t u$. The work extends previously known results for bounded domains in finite energy case. Furthermore, well-posedness and existence of locally-compact smooth attractors for the critical quintic non-linearity are obtained under less restrictive assumptions on non-linearity, relaxing some artificial technical conditions used before. This is achieved by virtue of new type Lyapunov functional that allow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04592","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":"1511.04592","created_at":"2026-05-18T01:26:52.245599+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.04592v1","created_at":"2026-05-18T01:26:52.245599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04592","created_at":"2026-05-18T01:26:52.245599+00:00"},{"alias_kind":"pith_short_12","alias_value":"WNNP3CMVR2HA","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WNNP3CMVR2HAPCKK","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WNNP3CMV","created_at":"2026-05-18T12:29:47.479230+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/WNNP3CMVR2HAPCKK7Q2L75CLJY","json":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY.json","graph_json":"https://pith.science/api/pith-number/WNNP3CMVR2HAPCKK7Q2L75CLJY/graph.json","events_json":"https://pith.science/api/pith-number/WNNP3CMVR2HAPCKK7Q2L75CLJY/events.json","paper":"https://pith.science/paper/WNNP3CMV"},"agent_actions":{"view_html":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY","download_json":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY.json","view_paper":"https://pith.science/paper/WNNP3CMV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.04592&json=true","fetch_graph":"https://pith.science/api/pith-number/WNNP3CMVR2HAPCKK7Q2L75CLJY/graph.json","fetch_events":"https://pith.science/api/pith-number/WNNP3CMVR2HAPCKK7Q2L75CLJY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY/action/storage_attestation","attest_author":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY/action/author_attestation","sign_citation":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY/action/citation_signature","submit_replication":"https://pith.science/pith/WNNP3CMVR2HAPCKK7Q2L75CLJY/action/replication_record"}},"created_at":"2026-05-18T01:26:52.245599+00:00","updated_at":"2026-05-18T01:26:52.245599+00:00"}