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.

Accepted:

DOI: 10.1051/m2an/2015080

Keywords: Multiscale analysis, peridynamics, nonlocal equations, Navier equation, homogenization, heterogeneous materials, two-scale convergence

^{1}; Lipton, Robert

^{2}; Mengesha, Tadele

^{3}

@article{M2AN_2016__50_5_1425_0, author = {Du, Qiang and Lipton, Robert and Mengesha, Tadele}, title = {Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1425--1455}, publisher = {EDP-Sciences}, volume = {50}, number = {5}, year = {2016}, doi = {10.1051/m2an/2015080}, zbl = {1348.74287}, mrnumber = {3554548}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015080/} }

TY - JOUR AU - Du, Qiang AU - Lipton, Robert AU - Mengesha, Tadele TI - Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1425 EP - 1455 VL - 50 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015080/ DO - 10.1051/m2an/2015080 LA - en ID - M2AN_2016__50_5_1425_0 ER -

%0 Journal Article %A Du, Qiang %A Lipton, Robert %A Mengesha, Tadele %T Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1425-1455 %V 50 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015080/ %R 10.1051/m2an/2015080 %G en %F M2AN_2016__50_5_1425_0

Du, Qiang; Lipton, Robert; Mengesha, Tadele. Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 5, pp. 1425-1455. doi : 10.1051/m2an/2015080. http://www.numdam.org/articles/10.1051/m2an/2015080/

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