Optimal convergence rate for homogenization of convex Hamilton-Jacobi equations in the periodic spatial-temporal environment

2022/12/30 by Hoang Nguyen-Tien, Nguyen-Tien, Hoang · 3 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2212.14782

openalex publication_date 2022/12/30 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28

Abstract

We study the optimal convergence rate for homogenization problem of convex Hamilton-Jacobi equations when the Hamitonian is periodic with respect to spatial and time variables, and notably time-dependent. We prove a result similar to that of [8], which means the optimal convergence rate is also O(ε).

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• Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions
• Quantitative homogenization of first-order ODEs
• Quantitative homogenization of convex Hamilton-Jacobi equations with u/ε-periodic Hamiltonians

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