Fast-Diffusion Limit for Reaction-Diffusion Equations with Degenerate Multiplicative and Additive Noise

摘要

In the present work we consider a quite general class of reaction-diffusion equations forced by additive and multiplicative noise. When the diffusion is large, one can approximate the solutions of the stochastic reaction-diffusion equations with polynomial term by the solutions of a stochastic ordinary equations with additive noise. We illustrate our results by applying it to logistic equation and nonlinear heat equation.