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

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.

Automated summary

In this study, we examine a general class of reaction-diffusion equations driven by additive and multiplicative noise. We show that for large diffusion, the solutions of stochastic reaction-diffusion equations with polynomial terms can be approximated by solutions of stochastic ordinary equations with additive noise. We demonstrate this with applications to the logistic equation and nonlinear heat equation.