{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZYPIBRUNFMYKMDQFTW4I5NHZNQ","short_pith_number":"pith:ZYPIBRUN","schema_version":"1.0","canonical_sha256":"ce1e80c68d2b30a60e059db88eb4f96c1cf71d92c39ad8e5300ea8f010d5be9f","source":{"kind":"arxiv","id":"1710.03408","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear diffusion equations as asymptotic limits of Cahn--Hilliard systems on unbounded domains via Cauchy's criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shunsuke Kurima, Takeshi Fukao, Tomomi Yokota","submitted_at":"2017-10-10T05:43:34Z","abstract_excerpt":"This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\in{\\mathbb N}$), written as\n  \\[\n  \\frac{\\partial u}{\\partial t} + (-\\Delta+1)\\beta(u)\n  = g \\quad \\mbox{in}\\ \\Omega\\times(0, T),\n  \\] which represents the porous media, the fast diffusion equations, etc., where $\\beta$ is a single-valued maximal monotone function on $\\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a gr"},"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":"1710.03408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-10T05:43:34Z","cross_cats_sorted":[],"title_canon_sha256":"533a59ed55b7be21fc9b8d6e2c4982e39ec3a502e5d269c6d6b5a0c415990666","abstract_canon_sha256":"5825f2187505605eeaeca3caf437b767552dce3d65d39ca61450f3d3ac8d501a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:30.966192Z","signature_b64":"AbjFCznXBBH7sA/SBqEZ65gaVbMkXi9f4fz9q1topucfTRV+hCxinVDdRkAXeez20vn9SWyKIHvGpJguUJjuBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce1e80c68d2b30a60e059db88eb4f96c1cf71d92c39ad8e5300ea8f010d5be9f","last_reissued_at":"2026-05-18T00:16:30.965657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:30.965657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear diffusion equations as asymptotic limits of Cahn--Hilliard systems on unbounded domains via Cauchy's criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shunsuke Kurima, Takeshi Fukao, Tomomi Yokota","submitted_at":"2017-10-10T05:43:34Z","abstract_excerpt":"This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\in{\\mathbb N}$), written as\n  \\[\n  \\frac{\\partial u}{\\partial t} + (-\\Delta+1)\\beta(u)\n  = g \\quad \\mbox{in}\\ \\Omega\\times(0, T),\n  \\] which represents the porous media, the fast diffusion equations, etc., where $\\beta$ is a single-valued maximal monotone function on $\\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03408","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":"1710.03408","created_at":"2026-05-18T00:16:30.965734+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.03408v1","created_at":"2026-05-18T00:16:30.965734+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03408","created_at":"2026-05-18T00:16:30.965734+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYPIBRUNFMYK","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYPIBRUNFMYKMDQF","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYPIBRUN","created_at":"2026-05-18T12:31:59.375834+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/ZYPIBRUNFMYKMDQFTW4I5NHZNQ","json":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ.json","graph_json":"https://pith.science/api/pith-number/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/graph.json","events_json":"https://pith.science/api/pith-number/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/events.json","paper":"https://pith.science/paper/ZYPIBRUN"},"agent_actions":{"view_html":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ","download_json":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ.json","view_paper":"https://pith.science/paper/ZYPIBRUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.03408&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/action/storage_attestation","attest_author":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/action/author_attestation","sign_citation":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/action/citation_signature","submit_replication":"https://pith.science/pith/ZYPIBRUNFMYKMDQFTW4I5NHZNQ/action/replication_record"}},"created_at":"2026-05-18T00:16:30.965734+00:00","updated_at":"2026-05-18T00:16:30.965734+00:00"}