Large deviation principles for multiscale stochastic Burgers equations with reflection

This study investigates multiscale stochastic Burgers equations with reflection, wherein the slow component is modeled by a stochastic Burgers equation with reflection and the fast component by a stochastic reaction-diffusion equation with reflection. Using the weak convergence approach, we rigorously establish a large deviation principle for the slow component. Key technical tools include the penalization method, carefully constructed stopping times, and a refined adaptation of Khasminskii’s classical time discretization scheme.