Title

Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media

Document Type

Article

Publication Date

9-1-2016

Abstract

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

First Page

1425

Last Page

1455

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