论文标题
ABC模型的流体动力学慢/快速边界
Hydrodynamics for the ABC model with slow/fast boundary
论文作者
论文摘要
在本文中，我们考虑与缓慢/快速储层接触的ABC模型。在此模型中，每个位点最多有一个粒子，它可以是$ {a，b，c \} $类型的$α\，而粒子在离散的点$ \ {1，\ cdots，n-1 \} $中交换位置与涉及交换机构类型的粒子类型。在边界点$ x = 1，n-1 $粒子可以以取决于涉及的粒子类型的速率注入或去除。我们证明，在扩散时间尺度上，流体动力学极限是由具有几个边界条件的非线性耦合方程式给出的，这取决于储层作用的强度。
In this article, we consider the ABC model in contact with slow/fast reservoirs. In this model, there is at most one particle per site, which can be of type $α\in\{A,B,C\}$ and particles exchange positions in the discrete set of points $\{1,\cdots, N-1\}$ with a weakly asymmetric rate that depends on the type of particles involved in the exchange mechanism. At the boundary points $x=1, N-1$ particles can be injected or removed with a rate that depends on the type of particles involved. We prove that the hydrodynamic limit, in the diffusive time scale, is given by a system of non-linear coupled equation with several boundary conditions, that depend on the strength of the reservoir's action.
