Quantitative homogenization of first-order ODEs

2025/08/25 by Ni, Panrui
#34A34 #35B27 #65L70 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17628

Abstract

This paper investigates the quantitative homogenization of first-order ODEs. For single-scale scalar ODEs, we obtain a sharp O(ε) convergence rate and characterize the effective constant. In the multi-scale setting, our results match those of \citeIM for long times but improve the short-time error to O(ε). We also initiate the study of quasi-periodic homogenization in this context. The scalar framework is further extended to higher dimensions under a boundedness assumption on trajectories. For weakly coupled systems with fast switching rates, we obtain for the first time a convergence rate of order O(ε). These results have applications to linear transport equations and broader connections to PDEs and gradient systems.

Citations

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