  This work is concerned with Freidlin-Wentzell type large deviation principle
for a family of multi-scale quasilinear and semilinear stochastic partial
differential equations. Employing the weak convergence method and Khasminskii's
time discretization approach, the Laplace principle (equivalently, large
deviation principle) for a general class of multi-scale SPDEs is derived. In
particular, we succeed in dropping the compactness assumption of embedding in
the Gelfand triple in order to deal with the case of bounded and unbounded
domains in applications. Our main results are applicable to various multi-scale
SPDE models such as stochastic porous media equations, stochastic p-Laplace
equations, stochastic fast-diffusion equations, stochastic 2D hydrodynamical
type models, stochastic power law fluid equations and stochastic Ladyzhenskaya
models.
