{"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. 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 "},"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"}