SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2718-2745, January 2021.
In this paper, we study the homogenization of a coupled diffusion-convection system. We consider a highly heterogeneous diffusion-convection equation in space, coupled with a stochastic differential equation with highly heterogeneous temporal scales that accounts for media change. Our main result consists of deriving the macroscale equation. We show that the resulting macroscale equation is deterministic with a nonlinear convective term. The convergence analysis involves the cell problem and the invariant measure of the stochastic differential equation. Although homogenization with changing media properties has been previously studied in other settings, this is the first result of this type, that includes a convective term. The latter makes the coupling between the homogenization and the time averaging much stronger. We show that the convergence to the limiting equation is in probability and we also find a corrector for it that gives stronger convergence.

中文翻译：

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对流扩散方程的随机均质化

SIAM数学分析杂志，第53卷，第3期，第2718-2745页，2021年1月。
在本文中，我们研究了耦合扩散对流系统的均质化。我们考虑空间中的高度异构扩散对流方程，再加上具有高度非均质时间尺度的随机微分方程，说明了介质变化。我们的主要结果包括推导宏观方程。我们表明，所产生的宏方程是具有非线性对流项的确定性。收敛分析涉及单元问题和随机微分方程的不变性度量。尽管先前已经在其他环境中研究了具有变化的介质特性的均质化，但这是这种类型的第一个结果，其中包括对流项。后者使均化和平均时间之间的耦合更强。