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

Abdellatif Benchérif-Madani; Étienne Pardoux

ESAIM: Probability and Statistics (2007)

- Volume: 11, page 385-411
- ISSN: 1292-8100

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topBenchérif-Madani, Abdellatif, and Pardoux, Étienne. "Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach." ESAIM: Probability and Statistics 11 (2007): 385-411. <http://eudml.org/doc/250095>.

@article{Benchérif2007,

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.
},

author = {Benchérif-Madani, Abdellatif, Pardoux, Étienne},

journal = {ESAIM: Probability and Statistics},

keywords = {Homogenization; nonlinear parabolic PDE; Poisson equation; diffusion approximation; backward SDE.; backward SDE; new ergodic theorems},

language = {eng},

month = {8},

pages = {385-411},

publisher = {EDP Sciences},

title = {Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach},

url = {http://eudml.org/doc/250095},

volume = {11},

year = {2007},

}

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

DA - 2007/8//

PB - EDP Sciences

VL - 11

SP - 385

EP - 411

AB -
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.

LA - eng

KW - Homogenization; nonlinear parabolic PDE; Poisson equation; diffusion approximation; backward SDE.; backward SDE; new ergodic theorems

UR - http://eudml.org/doc/250095

ER -

## References

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- E. Pardoux, Homogenization of linear and semilinear second order Parabolic PDEs with periodic coefficients: -a probabilistic approach. J. Func. Anal.167 (1999a) 498–520.
- E. Pardoux, BSDEs, weak convergence and homogenization of semilinear PDEs, in Nonlinear analysis, Differential Equations and Control, F.H. Clarke and R.J. Stern Eds., Kluwer Acad. Pub. (1999b) 503–549.

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