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.
Accepté le :
DOI : 10.1051/m2an/2015080
Mots clés : Multiscale analysis, peridynamics, nonlocal equations, Navier equation, homogenization, heterogeneous materials, two-scale convergence
@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 , Tome 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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