随机介质和开放边界中的格子气模型：流体动力学和弛豫到稳态
Lattice gas model in random medium and open boundaries: hydrodynamic and relaxation to the steady state
摘要：
本文考虑在由i.i.d.给出的随机场中，格气按不相容规则相互作用。有界区域中的有界随机变量与不同密度的颗粒储层接触。我们表明，在尺寸$d \ge 3$，重新缩放的经验密度场几乎肯定，相对于随机场，收敛到唯一的弱解的非线性抛物型方程的扩散矩阵由外部随机场的统计特性和边界条件所确定的水库的密度。此外，我们表明，重标度的经验密度场，在固定制度，几乎肯定相对于随机场，收敛到相关的固定输运方程的解决方案。
英文摘要：
We consider a lattice gas interacting by the exclusion rule in the presence of a random field given by i.i.d. bounded random variables in a bounded domain in contact with particles reservoir at different densities. We show, in dimensions $d \ge 3$, that the rescaled empirical density field almost surely, with respect to the random field, converges to the unique weak solution of a non linear parabolic equation having the diffusion matrix determined by the statistical properties of the external random field and boundary conditions determined by the density of the reservoir. Further we show that the rescaled empirical density field, in the stationary regime, almost surely with respect to the random field, converges to the solution of the associated stationary transport equation.
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