A microscopic mechanism for the porous medium equation

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• 作者：Feng ; Shui ; Iscoe ; Ian ; Sepp&auml ; l&auml ; inen ; Timo
• 关键词：Porous medium equation ; Hydrodynamic scaling limit
• 刊名：Stochastic Processes and their Applications
• 出版年：1997
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：March 28, 1997
• 卷：66
• 期：2
• 页码：147-182
• 文件大小：1.24 M

摘要

The porous medium equation on a d-dimensional torus is obtained as a hydrodynamic scaling limit, with the usual diffusion scaling, of the empirical measures of a sequence of reversible Markov jump processes on approximating periodic lattices. Each process can be viewed as a randomly interacting configuration of sticks (or energies, etc.). The configuration evolves through exchanges of stick portions that occur between nearest neighbours through a zero-range pressure mechanism, with conservation of total sticklength.