Large deviations for quasilinear parabolic stochastic partial differential equations

TL;DR

This paper proves large deviation principles for a class of complex quasilinear parabolic SPDEs with multiplicative noise, expanding the theoretical understanding of their probabilistic behavior.

Contribution

It introduces a novel application of the weak convergence approach to establish large deviations for non-monotone quasilinear parabolic SPDEs.

Findings

Established large deviation principles for complex SPDEs with multiplicative noise.

Extended the theoretical framework to non-monotone quasilinear parabolic equations.

Provided a new methodological approach using weak convergence.

Abstract

In this paper, we establish the Freidlin-Wentzell's large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The proof is based on the weak convergence approach.