In this paper, a singular semi-linear parabolic PDE with locally periodic coefficients is homogenized. We substantially weaken previous assumptions on the coefficients. In particular, we prove new ergodic theorems. We show that in such a weak setting on the coefficients, the proper statement of the homogenization property concerns viscosity solutions, though we need a bounded Lipschitz terminal condition.
Mots-clés : homogenization, nonlinear parabolic PDE, Poisson equation, diffusion approximation, backward SDE
@article{PS_2007__11__385_0,
author = {Bench\'erif-Madani, Abdellatif and Pardoux, \'Etienne},
title = {Homogenization of a semilinear parabolic {PDE} with locally periodic coefficients : a probabilistic approach},
journal = {ESAIM: Probability and Statistics},
pages = {385--411},
publisher = {EDP-Sciences},
volume = {11},
year = {2007},
doi = {10.1051/ps:2007026},
mrnumber = {2339300},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps:2007026/}
}
TY - JOUR AU - Benchérif-Madani, Abdellatif AU - Pardoux, Étienne TI - Homogenization of a semilinear parabolic PDE with locally periodic coefficients : a probabilistic approach JO - ESAIM: Probability and Statistics PY - 2007 SP - 385 EP - 411 VL - 11 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2007026/ DO - 10.1051/ps:2007026 LA - en ID - PS_2007__11__385_0 ER -
%0 Journal Article %A Benchérif-Madani, Abdellatif %A Pardoux, Étienne %T Homogenization of a semilinear parabolic PDE with locally periodic coefficients : a probabilistic approach %J ESAIM: Probability and Statistics %D 2007 %P 385-411 %V 11 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2007026/ %R 10.1051/ps:2007026 %G en %F PS_2007__11__385_0
Benchérif-Madani, Abdellatif; Pardoux, Étienne. Homogenization of a semilinear parabolic PDE with locally periodic coefficients : a probabilistic approach. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 385-411. doi : 10.1051/ps:2007026. http://archive.numdam.org/articles/10.1051/ps:2007026/
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