ESAIM: P&S, August 2007, Vol. 11, pp. 385-411
DOI: 10.1051/ps:2007026

Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach

Abdellatif Benchérif-Madani¹ and Étienne Pardoux<sup>2

1</sup>  Université Ferhat Abbas, Fac. Sciences, Dépt. Maths., Sétif 19000, Algeria; lotfi_madani@yahoo.fr
²  CMI, LATP - CNRS and Université de Provence, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France; pardoux@latp.unimrs.fr

(Received March 28, 2006. Revised December 6, 2006. Published online 17 August 2007.)

Abstract
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.

Mathematics Subject Classification. 35B27, 60H30, 60J60, 60J35

Key words: Homogenization, nonlinear parabolic PDE, Poisson equation, diffusion approximation, backward SDE.


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