Fast-diffusion limit for reaction-diffusion equations with multiplicative noise

Abstract

In this paper we consider a class of a stochastic partial differential equations with multiplicative noise and consider the limit of fast diffusion or other fast elliptic operator. We show that one can approximate solutions of the stochastic partial differential equations by the solution of a suitable stochastic ordinary differential equations on the kernel of the linear operator. We focus on equations with polynomial nonlinearities and give applications to Fisher–Kolmogorov–Petrovsky–Piscounov equation and the Ginzburg–Landau equation.