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arXiv · 2405.01408

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

Yuxi Han·Wenjia Jing·Hiroyoshi Mitake·Hung V. Tran
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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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Yuxi Han, Wenjia Jing, Hiroyoshi Mitake, Hung V. Tran. 2024-05-02. Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications. https://arxiv.org/abs/2405.01408

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