Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 4

Stochastic Σ-convergence and applications

Pages: 261 – 310

DOI: http://dx.doi.org/10.4310/DPDE.2011.v8.n4.a1

Authors

Mamadou Sango (Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa)

Jean Louis Woukeng (Department of Mathematics and Computer Science, University of Dschang, Cameroon)

Abstract

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 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.

Keywords

dynamical system, homogenization supralgebras, stochastic Σ-convergence, Stokes equations

2010 Mathematics Subject Classification

35B40, 35J25, 35R60, 46J10, 60H25

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