Effective Macroscopic Stochastic Models for Chemical Reactive Flows in Porous Media

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The aim of this work is to present new results on the study of macroscopic behaviour of chemical reactive flows acting under the influence of external random fluctuations through porous media. This porous media is made up of the fluid phase (pores) and the solid phase (skeleton), Diffusion takes places in the fluid phase while reaction takes place on the surface of the solid phase. The model of these phenomena comprises of a stochastic diffusion system in the fluid phase, a stochastic reaction system on the surface of the skeleton and a boundary condition coupling them. The main tools in obtaining the desired results, we first obtain appropriate energy estimates in suitable topological probabilistic spaces and use extension operators and homogenization techniques so that we work on a fixed domain. We show that as the pores goes to zero a homogenized model is obtain in a fixed domain.

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