Nous étudions l'homogénéisation d'opérateurs paraboliques du second ordre sous forme divergence à coefficients localement stationnaires. Ces coefficients présentent deux échelles d'évolution: une évolution microscopique presque constante et une évolution macroscopique régulière. La théorie de l'homogénéisation consiste à donner une approximation macroscopique de l'opérateur initial qui tient compte des hétérogénéités microscopiques. Cet article fait suite à [Probab. Theory Related Fields (2009)] et généralise ce dernier en considérant des matrices de diffusion pouvant dégénérer.
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by considering possibly degenerate diffusion matrices.
Mots clés : homogenization, random medium, degenerate diffusion, locally stationary environment
@article{AIHPB_2009__45_4_981_0, author = {Rhodes, R\'emi}, title = {Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {981--1001}, publisher = {Gauthier-Villars}, volume = {45}, number = {4}, year = {2009}, doi = {10.1214/08-AIHP190}, mrnumber = {2572160}, zbl = {1207.60029}, language = {en}, url = {http://www.numdam.org/articles/10.1214/08-AIHP190/} }
TY - JOUR AU - Rhodes, Rémi TI - Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2009 SP - 981 EP - 1001 VL - 45 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/08-AIHP190/ DO - 10.1214/08-AIHP190 LA - en ID - AIHPB_2009__45_4_981_0 ER -
%0 Journal Article %A Rhodes, Rémi %T Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix %J Annales de l'I.H.P. Probabilités et statistiques %D 2009 %P 981-1001 %V 45 %N 4 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/08-AIHP190/ %R 10.1214/08-AIHP190 %G en %F AIHPB_2009__45_4_981_0
Rhodes, Rémi. Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4, pp. 981-1001. doi : 10.1214/08-AIHP190. http://www.numdam.org/articles/10.1214/08-AIHP190/
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