Asymptotic Behavior Of Solutions For Kinds Of Stochastic Partial Differential Equations

This paper focuses on the dynamical behavior of serval kinds of stochastic partial differential equations with important application background. It is not only important in theory but also in application to investigate the existence of attractor of partial dif-ferential equations with white noise. And random attractors which includes L2-random attractor,Lp-random attractor, D-pullback attractor and D-period attractor are used to depict the asymptotic behavior of different kinds of stochastic partial differential equa-tions. The framework of this paper are following.In the first chapter, we mainly introduce the status of stochastic partial differential equations and some basic concepts and important results associated with the corre-sponding random dynamical system. Meanwhile, some classical inequalities, such as Cauchy inequality as well as an important transformation i.e., the Ornstein-Uhlenbeck transformation will be presented in this section.In the second chapter, we study the asymptotic behavior of random dynamical sys-tem generated by Fitzhugh-Nagumo equation with multiplicative white noise defined on unbounded domains and prove the existence of L2-random attractor of the corre-sponding random dynamical system by the tail-off method.In the third chapter, we investigate the dynamical behavior of random dynamical system generated by Reaction-Diffusion equation with multiplicative white noise de-fined on unbounded domains and establishes the existence of Lp-random attractor of corresponding random dynamical system by the asymptotic prior estimate.In the forth chapter, we devote to the research status of non-autonomous dynami-cal system and the proof of D-pullback attractor of Benjamin-Bona-Mahony equation with both non-autonomous term as well as random term.In the fifth chapter, we focus on the research status at home and abroad sine-Gordon equation and prove the existence of D-period attractor of the corresponding dynamical system associated with non-autonomous sine-Gordon equation.In the sixth chapter, we summarize the conclusions obtained in this paper and put forward problem remaining to be solved.