Geodesic
Homogenization of a semilinear parabolic PDE with locally periodic coefficients : a probabilistic approach
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 385-411

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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.

DOI : 10.1051/ps:2007026
Classification : 35B27, 60H30, 60J60, 60J35
Keywords: 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://geodesic.mathdoc.fr/articles/10.1051/ps:2007026/}
}
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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

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