Hydrodynamic Limit of Condensing Two-Species Zero Range Processes with Sub-critical Initial Profiles.
Hydrodynamic Limit of Condensing Two-Species Zero Range Processes with Sub-critical Initial Profiles.
复制标题
具有亚临界初始剖面的两种物质零程过程的流体动力学极限。
DOI：
10.1007/s10955-017-1827-6
复制
发表时间：
2017
影响因子：
1.6
通讯作者：
Dirr N
中科院分区：
文献类型：
--
作者：
Dirr N
两组分凝聚零程过程（Two-Species Condensing Zero Range Process，ZRP）是指两组分零程相互作用的粒子系统，在亚临界密度区域外表现出相分离。本文证明了具有有界局部跳跃率的最近邻平均零两组分凝聚ZRP在亚临界初始剖面下的流体动力学极限，即，对于图像包含在亚临界密度区域中的初始轮廓。证明是基于H. T。Yau的相对熵方法，它依赖于流体动力学方程的充分正则解的存在性。在特定的情况下，种盲ZRP，我们证明了流体动力学方程的解决方案存在于全球的时间，从而流体动力学限制是有效的所有时间。
Two-species condensing zero range processes (ZRPs) are interacting particle systems with two species of particles and zero range interaction exhibiting phase separation outside a domain of sub-critical densities. We prove the hydrodynamic limit of nearest neighbour mean zero two-species condensing ZRP with bounded local jump rate for sub-critical initial profiles, i.e., for initial profiles whose image is contained in the region of sub-critical densities. The proof is based on H.T. Yau’s relative entropy method, which relies on the existence of sufficiently regular solutions to the hydrodynamic equation. In the particular case of the species-blind ZRP, we prove that the solutions of the hydrodynamic equation exist globally in time and thus the hydrodynamic limit is valid for all times.