The D-pullback Attractor For Two Kinds Of Wave Equations With White Noise And Memory Term

This dissertation discusses about D-pullback attractors for two kinds of stochastic wave equations with multiplicative(additive) noise. The random attractor is an important tool of the dynamic behavior of the stochastic differential equation. It is not only important in the theory but also in application to investigate the existence of Dpullback attractor of stochastic evolution equations with multiplication(additive) noise.The framework of this paper are following.In the first chapter, we mainly sketch the history and the development of random dynamical system, random attractor, D-pullback attractor and D-period attractor.Meanwhile, some preliminary results and definitions and classical inequalities as well as an important transformation which used in this paper i.e., the Ornstein-Uhlenbeck transformation will be presented in this section.In the second chapter, we study the non-autonomous sine-Gordon equation with memory term and establishes the existence of D-period attractor of corresponding dynamical system associated with non-autonomous sine-Gordon equation with memory term.In the third chapter, we consider the asymptotic behavior of random dynamical system generated by non-autonomous wave equation with multiplicative white noise and memory term and prove the existence of random attractor of the corresponding random dynamical system.In the forth chapter, we summarize the conclusions obtained in this paper and put forward problem remaining to be solved.