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

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

Full Text (PDF format)

Published 20 September 2013