{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:M7NYAY55ONTYQL4K3YRGVNXHSQ","short_pith_number":"pith:M7NYAY55","schema_version":"1.0","canonical_sha256":"67db8063bd7367882f8ade226ab6e79420966f6e6a6d75754adf9448d6a324c5","source":{"kind":"arxiv","id":"1502.06383","version":2},"attestation_state":"computed","paper":{"title":"Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Segatti, Giulio Schimperna, Goro Akagi","submitted_at":"2015-02-23T10:59:02Z","abstract_excerpt":"We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain $\\Omega$ of $R^N$ and complemented with homogeneous Dirichlet boundary conditions of solid type (i.e., imposed in the entire complement of $\\Omega$). After setting a proper functional framework, we prove existence and uniqueness of weak solutions to the related initial-boundary value problem. Then, we investigate some significant singular limits obtained as the order of either of the fractional Laplacians appearing in the equation is let tend to 0. In particular, we can rigorously prove that the fractio"},"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":"1502.06383","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-23T10:59:02Z","cross_cats_sorted":[],"title_canon_sha256":"c68fc611b37b25c2e5112ab491b2c0f09d40644f16b54d8dd6bb8b51ede5069c","abstract_canon_sha256":"46e401232e97cb1b5168f890b3ab59d5e01070ed9b6a573e8d898967073532d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:33.643473Z","signature_b64":"yP1fFvbNKs96PzLUrYv1MqWyGm6kldGiRfjQDpPMdyKhK07v+E17khUC9pGW3hHoeY6C/LjosNzIVbw5Nqh9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67db8063bd7367882f8ade226ab6e79420966f6e6a6d75754adf9448d6a324c5","last_reissued_at":"2026-05-18T02:25:33.643051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:33.643051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Segatti, Giulio Schimperna, Goro Akagi","submitted_at":"2015-02-23T10:59:02Z","abstract_excerpt":"We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain $\\Omega$ of $R^N$ and complemented with homogeneous Dirichlet boundary conditions of solid type (i.e., imposed in the entire complement of $\\Omega$). After setting a proper functional framework, we prove existence and uniqueness of weak solutions to the related initial-boundary value problem. Then, we investigate some significant singular limits obtained as the order of either of the fractional Laplacians appearing in the equation is let tend to 0. In particular, we can rigorously prove that the fractio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06383","kind":"arxiv","version":2},"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":"1502.06383","created_at":"2026-05-18T02:25:33.643111+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06383v2","created_at":"2026-05-18T02:25:33.643111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06383","created_at":"2026-05-18T02:25:33.643111+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7NYAY55ONTY","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7NYAY55ONTYQL4K","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7NYAY55","created_at":"2026-05-18T12:29:32.376354+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/M7NYAY55ONTYQL4K3YRGVNXHSQ","json":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ.json","graph_json":"https://pith.science/api/pith-number/M7NYAY55ONTYQL4K3YRGVNXHSQ/graph.json","events_json":"https://pith.science/api/pith-number/M7NYAY55ONTYQL4K3YRGVNXHSQ/events.json","paper":"https://pith.science/paper/M7NYAY55"},"agent_actions":{"view_html":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ","download_json":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ.json","view_paper":"https://pith.science/paper/M7NYAY55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06383&json=true","fetch_graph":"https://pith.science/api/pith-number/M7NYAY55ONTYQL4K3YRGVNXHSQ/graph.json","fetch_events":"https://pith.science/api/pith-number/M7NYAY55ONTYQL4K3YRGVNXHSQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ/action/storage_attestation","attest_author":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ/action/author_attestation","sign_citation":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ/action/citation_signature","submit_replication":"https://pith.science/pith/M7NYAY55ONTYQL4K3YRGVNXHSQ/action/replication_record"}},"created_at":"2026-05-18T02:25:33.643111+00:00","updated_at":"2026-05-18T02:25:33.643111+00:00"}