Large Deviation Principle For Stochastic Burgers Type Equation With Reflection

In this paper,we study two kinds of stochastic partial differential equations,namely,the reflected stochastic Burgers partial differential equation with small perturbation and the stochastic heat equation driven by white-fractional Gaussian noise.As for the stochastic Burgers equation,the main task is to prove its large deviation principle.The main difficulties of this work are the high nonlinearity of the term of the equation and the singularity caused by reflection.Recently,Matoussi,Sabbagh and Zhang put forward a sufficient condition for the weak convergence method in[26].After discussion,it is found that this sufficient condition is very suitable to deal with stochastic dynamical problems and large deviation principle of reflected stochastic ordinary(partial)differential equations.Therefore,we adopt this sufficient condition and obtain the large deviation principle of stochastic Burgers equation.As for the stochastic heat equation,the main work is to discuss the decomposition of the stochastic convolution in time and space and get the specific decomposition coefficient.Let u={u(t,x);(t,x)?R+×R} be the solution to a linear stochastic heat equation driven by white-fractional Gaussian noise,We prove that for any given x ? R(resp.t ? R+),the stochastic process t ? u(t,x)(resp.x ? u(t,x))can be decomposed into fractional Brownian motions with Hurst parameter H/2(resp.H)plus a stochastic process with C?-continuous trajectories.In addition,some inferences of stochastic convolution decomposition will also be discussed in this article.