Quantitative homogenization of first-order ODEs
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915461166268416 |
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| author | Ni, Panrui |
| author_facet | Ni, Panrui |
| contents | This paper investigates the quantitative homogenization of first-order ODEs. For single-scale scalar ODEs, we obtain a sharp $O(\varepsilon)$ convergence rate and characterize the effective constant. In the multi-scale setting, our results match those of \cite{IM} for long times but improve the short-time error to $O(\varepsilon)$. 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 $O(\varepsilon)$. These results have applications to linear transport equations and broader connections to PDEs and gradient systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative homogenization of first-order ODEs Ni, Panrui Classical Analysis and ODEs Analysis of PDEs 35B27, 34A34, 65L70 This paper investigates the quantitative homogenization of first-order ODEs. For single-scale scalar ODEs, we obtain a sharp $O(\varepsilon)$ convergence rate and characterize the effective constant. In the multi-scale setting, our results match those of \cite{IM} for long times but improve the short-time error to $O(\varepsilon)$. 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 $O(\varepsilon)$. These results have applications to linear transport equations and broader connections to PDEs and gradient systems. |
| title | Quantitative homogenization of first-order ODEs |
| topic | Classical Analysis and ODEs Analysis of PDEs 35B27, 34A34, 65L70 |
| url | https://arxiv.org/abs/2508.17628 |