Large deviations for stochastic porous media equations

In this paper, we establish the Freidlin-Wentzell type large deviation principles for porous medium-type equations perturbed by small multiplicative noise. The porous medium operator $\mathrm{\Delta }(\mathrm{\mid }u{\mathrm{\mid }}^{m-1}u)$ is allowed. Our proof is based on weak convergence approach.