Exponential Attractors For Several Classes Of Stochastic Systems

In this dissertation we propose the concept of random uniform exponential attrac-tors for non-autonomous random dynamical systems,and study the existence of random exponential attractors and random uniform exponential attractors for several classes of non-autonomous stochastic systems.Moreover,we study the existence of a random uni-form attractor and a random cocycle attractor for a stochastic systemsIn chapter 1,we first introduce the development of the research on attractors for non-autonomous random dynamical systems,and the background of the studied Navier-Stokes equation,damped Navier-Stokes equation,FitzHugh-Nagumo system,reaction-diffusion equation,lattice dynamical system and FitzHugh-Nagumo lattice dynamical system as well as their research development on different kinds of attractors.Then we present the main results obtained in this dissertation.At last,we give some basic tools used in this dissertation.In chapter 2,we first give the existence criteria of random exponential attractors for non-autonomous random dynamical systems,then we propose the concept of random uniform exponential attractors and its existence criteriaIn chapter 3,we first study the existence of a random exponential attractor for 2D non-autonomous Navier-Stokes equation with additive noise defined on bounded do-mains,then study the existence of a random uniform exponential attractor for 2D non-autonomous Navier-Stokes equation with additive noise and quasi-periodic force defined on bounded domains.Finally,we study the existence of a random exponential attractor for 3D non-autonomous damped Navier-Stokes equation with additive noise defined on bounded domainsIn chapter 4,we first study the existence of a random exponential attractor for non-autonomous FitzHugh-Nagumo system with multiplicative noise defined on entire space,then we study the existence of a random exponential attractor for non-autonomous FitzHugh-Nagumo system with additive noise defined on entire space.Finally,we study the existence of a random uniform exponential attractor for non-autonomous FitzHugh-Nagumo system with additive noise and quasi-periodic force defined on entire spaceIn chapter 5,we study the existence of a random uniform exponential attractor for non-autonomous reaction diffusion equation with multiplicative noise and quasi-periodic force defined on entire spaceIn chapter 6,we study the existence of random uniform exponential attractors for non-autonomous lattice system and FitzHugh-Nagumo lattice system with multiplicative noise and quasi-periodic forceIn chapter 7,we study the existence of a random uniform attractor and a random cocycle attractor for non-autonomous FitzHugh-Nagumo system with multiplicative noise defined on entire spaceIn chapter 8,we summarize the results obtained in this dissertation and propose several problems for further investigation.