Averaging Principle For One Dimensional Stochastic Burgers Equation With Lévy Noise

The averaging principle is an important method to study the dynamics model of fast-slow system,which is widely applied to the dynamics research because of its sim-plicity,dimensionality reduction,and high efficiency.Therefore,the study of the prin-ciple of averaging has important scientific significance and practical guiding value.We consider the averaging principle for one dimensional stochastic Burgers equa-tion with Levy noise and give the rate of the slow component converges to the solution of the averaged equation:#12 It is divided into the following steps specifically:First,we give some priori estimates of(Xt?,Yt?).Second,for given ?>0,T>0,we divide the interval into[k?,(k+1)?)and construct an auxiliary(Xt?,Yt?),l?[k?,(k+1)?),which we also give the uniform bounds.Meanwhile,we deduce an estimate of the process Xt?-Xt? in the space L2p(?,C([0,T],L2)).Third,we make use of the skill of the stopping time and some approximation techniques to give a control of |Xt?-Xt?|L2p(?,C[0,T],L2))and deduce the convergence rate.The biggest challenge encountered in the proof process is to deal with nonlinear terms,we can further obtain sup0<?<1 E supo?t?T |Xt?|?p?Cp,T by using the smoothness of semigroup et? and interpolation inequality.