Abstract
We consider a problem of transport of a physical entity by an incompressible velocity in a domain composed of a fixed region and thin varying layers. We suppose that these layers display a cellular microstructure with random thin varying thickness. We suppose that, within the layers, the diffusion and velocity coefficients admit random large-scale structures. Under mixing properties of the diffusion and velocity processes we study the asymptotic behavior of the problem with respect to a vanishing parameter describing the thickness of the layers. We derive the effective boundary conditions on the boundary of the fixed region. These boundary conditions reveal the effects of the random time fluctuations of the diffusion coefficient and fluid velocity.
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