Application of Markov Chain Approximation Method to Nonlinear Diffusion Equation

Abstract

We consider the high density scaling limit of a stochastic model for nonlinear diffusion which is constructed as a random walk on the discrete torus with a nonlinear diffusion rates. In this paper, we show that the deterministic limit of the stochastic model is governed by the nonlinear diffusion equation by showing the relative compactness and using the continuous mapping theorem.