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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. 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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. 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