We analyze the hydrodynamic behavior of the porous medium model (PMM) in a discrete space $$\{0,\ldots , n\}$$ { 0 , … , n } , where the sites 0 and n stand for reservoirs. Our strategy relies on the entropy method of Guo et al. (Commun Math Phys 118:31–59, 1988). However, this method cannot be straightforwardly applied, since there are configurations that do not evolve according to the dynamics (blocked configurations). In order to avoid this problem, we slightly perturbed the dynamics in such a way that the macroscopic behavior of the system keeps following the porous medium equation (PME), but with boundary conditions which depend on the reservoirs’ strength.

中文翻译：

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具有慢速储层的多孔介质模型的流体动力学

我们在离散空间 $$\{0,\ldots , n\}$$ { 0 , … , n } 中分析多孔介质模型 (PMM) 的流体动力学行为，其中位点 0 和 n 代表储层。我们的策略依赖于郭等人的熵方法。(Commun Math Phys 118:31-59, 1988)。然而，这种方法不能直接应用，因为有些配置不会根据动态演变（阻塞配置）。为了避免这个问题，我们稍微扰动了动力学，使系统的宏观行为保持遵循多孔介质方程 (PME)，但边界条件取决于储层的强度。