{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XPP6DNFUEEYLGS33XZN7IH3XGK","short_pith_number":"pith:XPP6DNFU","schema_version":"1.0","canonical_sha256":"bbdfe1b4b42130b34b7bbe5bf41f77328dee8484199210a39dae44d52f6c4e74","source":{"kind":"arxiv","id":"1110.6262","version":1},"attestation_state":"computed","paper":{"title":"A gradient flow approach to a thin film approximation of the Muskat problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bogdan-Vasile Matioc, Philippe Laurencot (IMT)","submitted_at":"2011-10-28T06:55:56Z","abstract_excerpt":"A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two Liapunov functionals turns out to be a central tool to obtain the needed regularity to identify the Euler-Lagrange equation in the variational scheme."},"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":"1110.6262","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-28T06:55:56Z","cross_cats_sorted":[],"title_canon_sha256":"662050b20e21c0584053a892a03ebe8c79220ea43e7b1a2cfc492fdd64f42280","abstract_canon_sha256":"e1076f4a211f2c0f1f98a3f2debdd0b77712615548bf7222d813dbd908c40ec7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:50.408768Z","signature_b64":"R3RFE1uOf8+j/8OnkeHkUmferul0l9J1y4wUTdP3qM94SjZd7ppGjB6sG2+T3RUh3mokL3rKwIQRztv3jVPIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbdfe1b4b42130b34b7bbe5bf41f77328dee8484199210a39dae44d52f6c4e74","last_reissued_at":"2026-05-18T03:14:50.408280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:50.408280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A gradient flow approach to a thin film approximation of the Muskat problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bogdan-Vasile Matioc, Philippe Laurencot (IMT)","submitted_at":"2011-10-28T06:55:56Z","abstract_excerpt":"A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two Liapunov functionals turns out to be a central tool to obtain the needed regularity to identify the Euler-Lagrange equation in the variational scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6262","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":"1110.6262","created_at":"2026-05-18T03:14:50.408352+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.6262v1","created_at":"2026-05-18T03:14:50.408352+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6262","created_at":"2026-05-18T03:14:50.408352+00:00"},{"alias_kind":"pith_short_12","alias_value":"XPP6DNFUEEYL","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"XPP6DNFUEEYLGS33","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"XPP6DNFU","created_at":"2026-05-18T12:26:47.523578+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/XPP6DNFUEEYLGS33XZN7IH3XGK","json":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK.json","graph_json":"https://pith.science/api/pith-number/XPP6DNFUEEYLGS33XZN7IH3XGK/graph.json","events_json":"https://pith.science/api/pith-number/XPP6DNFUEEYLGS33XZN7IH3XGK/events.json","paper":"https://pith.science/paper/XPP6DNFU"},"agent_actions":{"view_html":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK","download_json":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK.json","view_paper":"https://pith.science/paper/XPP6DNFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.6262&json=true","fetch_graph":"https://pith.science/api/pith-number/XPP6DNFUEEYLGS33XZN7IH3XGK/graph.json","fetch_events":"https://pith.science/api/pith-number/XPP6DNFUEEYLGS33XZN7IH3XGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK/action/storage_attestation","attest_author":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK/action/author_attestation","sign_citation":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK/action/citation_signature","submit_replication":"https://pith.science/pith/XPP6DNFUEEYLGS33XZN7IH3XGK/action/replication_record"}},"created_at":"2026-05-18T03:14:50.408352+00:00","updated_at":"2026-05-18T03:14:50.408352+00:00"}