Study About Long Time Behavior Of Two Kinds Of Lattice Systems Driven By Nonlinear Noise

This paper mainly studies the long-time behavior of solutions of nonautonomous long and short wave lattice systems and Schr(?)dinger-Boussinesq lattice systems driven by nonlinear noise.The existence and uniqueness of weak pullback mean random attractors for two kinds of equations are proved.In addition,the existence of invariant measures of average stochastic dynamical systems generated by two kinds of equations is proved.The first chapter mainly introduces the research background and current situation of stochastic dynamical systems,briefly summarizes the main work of this paper and briefly introduces some preliminary knowledge.In Chapter 2,we study the existence of weak pullback mean stochastic attractors and invariant measures of the average stochastic dynamic system generated by the lattice system corresponding to the stochastic long short wave equation driven by nonlinear noise.In Chapter 3,we study the existence of weak pullback mean random attractors and invariant measures for the average random dynamic system generated by the lattice system corresponding to the stochastic Schr(?)dinger-Boussinesq equation with nonlinear noise term.The fourth chapter summarizes the main research contents of this paper and points out the problems that can be further discussed.