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nonlinear parabolic pde

ESAIM: Probability and Statistics (1)

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Homogenization of a semilinear parabolic PDE with locally periodiccoefficients: a probabilistic approach
Abdellatif Benchérif-Madani, Étienne Pardoux
Journal:

ESAIM: Probability and Statistics / Volume 11 / June 2007

Published online by Cambridge University Press:

17 August 2007, pp. 385-411

Print publication:

June 2007
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In this paper, a singular semi-linear parabolic PDE with locally periodiccoefficients is homogenized. We substantially weaken previous assumptions onthe coefficients. In particular, we prove new ergodic theorems. We show thatin such a weak setting on the coefficients, the proper statement of thehomogenization property concerns viscosity solutions, though we need abounded Lipschitz terminal condition.