Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications

2024/05/02 by Yuxi Han, Han, Yuxi, Wenjia Jing +5 · 4 citations
Computer Science · Engineering · #35B10 #35B27 #35B40 #35F21 #49L25 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2405.01408

openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the periodic homogenization problem of state-constraint Hamilton--Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We then consider a dilute situation in which the holes' diameter is much smaller than the microscopic scale. Finally, a homogenization problem with domain defects where some holes are missing is analyzed.

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