Dominant dynamics for a class of singularly perturbed stochastic partial differential equations with quadratic nonlinearities and random Neumann boundary conditions

This work concerns the effective approximation for a class of singularly perturbed stochastic partial differential equations driven by a sufficiently small multiplicative noise with quadratic nonlinearities and random Neumann boundary conditions. By splitting the solution into two parts in the finite dimension kernel space and its complement space with some suitable multi-scale argument, it derives rigorously the dominant dynamics, which captures the essential dynamics of the original system as a singular parameter is enough small.