Calculus of Variations and Geometric Measure Theory

M. Duerinckx - A. Gloria - M. Ruf

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

created by ruf on 28 Mar 2023



Inserted: 28 mar 2023

Year: 2023

ArXiv: 2303.07684 PDF


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 the introduction of 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 sets of assumptions on heterogeneities (both periodic and stationary random settings).