A spectral ansatz for the long-time homogenization of the wave equation

Autor:	Duerinckx, Mitia, Gloria, Antoine, Ruf, Matthias
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics 35B27 35B40 35C20 35L05 74Q10 74Q15 74H40 35B30 35P05
Druh dokumentu:	Working Paper
Popis:	Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present work is a new ansatz for the long-time two-scale expansion inspired by spectral analysis. Based on this spectral ansatz, we extend and refine all previous results in the field, proving homogenization up to optimal timescales with optimal error estimates, and covering all the standard assumptions on heterogeneities (both periodic and stationary random settings). Comment: published version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.07684 Zobrazit plný text záznamu View this record from Arxiv