{"paper":{"title":"Homogenization of Viscous Sublinear Hamilton--Jacobi Equations with $u/\\epsilon$-Dependence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guyu Jin","submitted_at":"2026-08-01T04:33:07Z","abstract_excerpt":"We study the periodic homogenization of a class of viscous Hamilton--Jacobi equations with fast dependence on the unknown. This problem combines features of first-order Hamilton--Jacobi equations with \\(u^\\epsilon/\\epsilon\\)-periodic Hamiltonians and semilinear heat equations with rapidly oscillating positive potentials. In this paper, we prove qualitative homogenization results for $H(y,s,p)=F(s,p)+\\eta W(y,s,p)$ when $|\\eta|$ is sufficiently small, with the smallness threshold depending on the Lipschitz constant of the initial datum, and establish a large-time averaging result for a general "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.00438","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/2608.00438/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"}