Stochastic Σ-convergence and applications

Mamadou Sango, Jean Louis Woukeng
2011 Dynamics of Partial Differential Equations  
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems simultaneously, and also separately. Our approach, the stochastic Σ-convergence, can be seen either as a multiscale stochastic approach since deterministic homogenization theory can be seen as a special case of stochastic homogenization theory (see Theorem 3), or
more » ... ee Theorem 3), or as a conjunction of the stochastic and deterministic approaches, both taken globally, but also each separately. One of the main applications of our results is the homogenization of a model of rotating fluids. 2000 Mathematics Subject Classification. 35J25, 35R60, 35B40, 46J10, 60H25.
doi:10.4310/dpde.2011.v8.n4.a1 fatcat:6xcnbtpwtrcanmzyh6cz2kmia4