The method of two scale convergence is implemented to study the homogenization of time-dependent nonlocal continuum models of heterogeneous media. Two integro-differential models are considered: the nonlocal convection-diffusion equation and the state-based peridynamic model in nonlocal continuum mechanics. The asymptotic analysis delivers both homogenized dynamics as well as strong approximations expressed in terms of a suitable corrector theory. The method provides a natural analog to that for the time-dependent local PDE models with highly oscillatory coefficients with the distinction that the driving operators considered in this work are bounded.
Publication Source (Journal or Book title)
ESAIM: Mathematical Modelling and Numerical Analysis
Du, Q., Lipton, R., & Mengesha, T. (2016). Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media. ESAIM: Mathematical Modelling and Numerical Analysis, 50 (5), 1425-1455. https://doi.org/10.1051/m2an/2015080