In this article, we explore Freidlin-Wentzell's large deviation principle for a stochastic partial differential equation with the nonlinear diffusion-convection operator in divergence form satisfying p-type growth, involving coercivity assumptions, perturbed by small multiplicative Brownian noise. We use the weak convergence method, to prove the Laplace principle, which is equivalent to the large deviation principle in our framework.
2020 Mathematics Subject Classification. 60H15, 35R60, 60F1