The purpose of this article is to provide a simple proof of the hydrodynamic and hydrostatic behavior of the SSEP in contact with slowed reservoirs which inject and remove particles in a finite size windows at the extremities of the bulk. More precisely, the reservoirs inject/remove particles at/from any point of a window of size K placed at each extremity of the bulk and particles are injected/removed to the first open/occupied position in that window. The hydrodynamic limit is given by the heat equation with non-linear Robin boundary conditions or Neumann boundary conditions, the latter being in the case when the reservoirs are too slow. The proof goes through the entropy method of Guo, Papanicolaou and Varadhan. We also derive the hydrostatic limit for this model, whose proof is based on the method developed by Landim and Tsunoda. We observe that we do not make use of correlation estimates in none of our results.

中文翻译：

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具有不可逆慢边界动力学的 SSEP 的流体动力学：第 I 部分，临界状态及以后

本文的目的是提供一个简单的证明，证明 SSEP 与缓慢的储层接触时的流体动力学和流体静力学行为，这些储层在体的末端以有限尺寸的窗口注入和去除颗粒。更准确地说，储存器在/从放置在主体的每个末端的大小为K的窗口的任何点处注入/去除颗粒，并且颗粒被注入/去除到该窗口中的第一打开/占据位置。水动力极限由具有非线性罗宾边界条件或诺依曼边界条件的热方程给出，后者是在储层太慢的情况下。证明通过郭、Papanicolaou 和 Varadhan 的熵方法。我们还推导出了该模型的静水极限，其证明基于 Landim 和 Tsunoda 开发的方法。