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# Communications in Mathematical Sciences

## Volume 12 (2014)

### Number 2

### Homogenization of stochastic semilinear parabolic equations with non-Lipschitz forcings in domains with fine grained boundaries

Pages: 345 – 382

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n2.a7

#### Author

#### Abstract

The present work deals with the homogenization and in-depth asymptotic analysis of a nonlinear stochastic evolution equation with non-Lipschitz nonlinearities in a domain with fine grained boundaries in which the obstacles have a non-periodic distribution. Under appropriate conditions on the data it is proved that a solution of the initial problem converges in suitable topologies to a solution of a limit problem which contains an additional term of capacity type. The notion of solution is that of weak probabilistic which is a system consisting of a probability space, Wiener process, and a solution in the distribution sense of the problem.

#### Keywords

stochastic partial differential equation, homogenization, perforated domains

#### 2010 Mathematics Subject Classification

35B27, 60H15