Stochastic heat equation with Burgers term driven by fractional noises with two reflecting walls

Abstract

In this article, we study stochastic heat equation with Burgers term with two reflecting walls h1 and h2, driven by space-time fractional noises. We will first show the existence and uniqueness of the solution by Picard iteration scheme, then we will consider the penalized approximating equations with respect to the reflecting terms to obtain the Hölder continuity of this solution. Furthermore, the large deviation principle for the law of the solution to this equation with a small perturbation will be established through a classical method.