{"paper":{"title":"Optimal rate of convergence in periodic homogenization of viscous Hamilton-Jacobi equations","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Hung V. Tran, Jianliang Qian, Timo Sprekeler, Yifeng Yu","submitted_at":"2024-02-05T15:23:04Z","abstract_excerpt":"We study the optimal rate of convergence in periodic homogenization of the viscous Hamilton-Jacobi equation $u^\\varepsilon_t + H(\\frac{x}{\\varepsilon},Du^\\varepsilon) = \\varepsilon \\Delta u^\\varepsilon$ in $\\mathbb R^n\\times (0,\\infty)$ subject to a given initial datum. We prove that $\\|u^\\varepsilon-u\\|_{L^\\infty(\\mathbb R^n \\times [0,T])} \\leq C(1+T) \\sqrt{\\varepsilon}$ for any given $T>0$, where $u$ is the viscosity solution of the effective problem. Moreover, we show that the $O(\\sqrt{\\varepsilon})$ rate is optimal for a natural class of $H$ and a Lipschitz continuous initial datum, both t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.03091","kind":"arxiv","version":2},"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/2402.03091/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"}