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Cuesta (2) ((1) LMAP-UMR CNRS 5142, Lo\\\"ic Constantin (1","submitted_at":"2025-07-01T17:08:21Z","abstract_excerpt":"In this paper we study a doubly degenerate parabolic equation involving a convection term and the operator $\\mathcal{A}_\\mu u:=-\\Delta_p u +\\mu (-\\Delta)^s_q u$ which is a linear combination of the $p$-Laplacian and the fractional $q$-Laplacian, and results in a mixed local-nonlocal nonlinear operator. The problem we study is the following, \\begin{equation*}\n  \\begin{cases}\n  \\partial_t \\beta(u)+ \\mathcal{A}_\\mu u= div (\\overset{\\to}{f}(u))+g(t,x,u) \\quad \\text{in} \\;Q_T:=(0,T)\\times \\Omega,\n  u=0 \\quad \\text{in} \\; (0,T)\\times (\\mathbb{R}^d \\backslash \\Omega),\n  u(0)=u_0 \\text{ in } \\Omega.\n "},"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":"2507.00959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-01T17:08:21Z","cross_cats_sorted":[],"title_canon_sha256":"49745a8f703f15f5b867abac71d5e44cc69db3726c14fd59e009d5c875f4654b","abstract_canon_sha256":"05a6e0b96787d1648ba77ef49e58ab819964f33efa8f18cd416868d566609d5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:30:18.628608Z","signature_b64":"l4QrrdgmimLih3okHTap+Xsy33+dd6+zPANMj3kze+UhtsI5wES3Kufui4+pkxlBAUWPQwsF5NW8uZLNx9jcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed22feefb083bc002c85d8fe6cc47e31c2d8136863f2bc48ac34386e2c3cb2be","last_reissued_at":"2026-07-05T11:30:18.628079Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:30:18.628079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Doubly nonlinear parabolic equation involving a mixed local-nonlocal operator and a convection term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"2), (2) UPV/EHU), Carlota M. 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The problem we study is the following, \\begin{equation*}\n  \\begin{cases}\n  \\partial_t \\beta(u)+ \\mathcal{A}_\\mu u= div (\\overset{\\to}{f}(u))+g(t,x,u) \\quad \\text{in} \\;Q_T:=(0,T)\\times \\Omega,\n  u=0 \\quad \\text{in} \\; (0,T)\\times (\\mathbb{R}^d \\backslash \\Omega),\n  u(0)=u_0 \\text{ in } \\Omega.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00959","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.00959/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.00959","created_at":"2026-07-05T11:30:18.628133+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.00959v1","created_at":"2026-07-05T11:30:18.628133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00959","created_at":"2026-07-05T11:30:18.628133+00:00"},{"alias_kind":"pith_short_12","alias_value":"5URP535QQO6A","created_at":"2026-07-05T11:30:18.628133+00:00"},{"alias_kind":"pith_short_16","alias_value":"5URP535QQO6AALEF","created_at":"2026-07-05T11:30:18.628133+00:00"},{"alias_kind":"pith_short_8","alias_value":"5URP535Q","created_at":"2026-07-05T11:30:18.628133+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/5URP535QQO6AALEF3D7GZRD6GH","json":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH.json","graph_json":"https://pith.science/api/pith-number/5URP535QQO6AALEF3D7GZRD6GH/graph.json","events_json":"https://pith.science/api/pith-number/5URP535QQO6AALEF3D7GZRD6GH/events.json","paper":"https://pith.science/paper/5URP535Q"},"agent_actions":{"view_html":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH","download_json":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH.json","view_paper":"https://pith.science/paper/5URP535Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.00959&json=true","fetch_graph":"https://pith.science/api/pith-number/5URP535QQO6AALEF3D7GZRD6GH/graph.json","fetch_events":"https://pith.science/api/pith-number/5URP535QQO6AALEF3D7GZRD6GH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH/action/storage_attestation","attest_author":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH/action/author_attestation","sign_citation":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH/action/citation_signature","submit_replication":"https://pith.science/pith/5URP535QQO6AALEF3D7GZRD6GH/action/replication_record"}},"created_at":"2026-07-05T11:30:18.628133+00:00","updated_at":"2026-07-05T11:30:18.628133+00:00"}