Uniform Large Deviations for Stochastic Generalized Burgers-Huxley Equation Driven by Multiplicative Noise

Abstract

In this paper, we establish a Freidlin-Wentzell type large deviation principle uniformly with respect to initial condition in bounded subsets, that do not necessarily belongs to compact sets, of an infinite dimensional Banach space for stochastic 1D generalized Burgers-Huxley equation driven by multiplicative small noise. The proof is based on the weak convergence approach obtained by [Budhiraja, Dupuis and Salins; Trans. Amer. Math. Soc., 2019].