THE LONG TIME BEHAVIOR FOR PARTLY DISSIPATIVE STOCHASTIC SYSTEMS

Abstract

In this paper, we consider the long time behaviors for the partly dissipative stochastic reaction diffusion equations in <i>D</i> &#8834; R^<i>n</i>. The main purpose of this paper is to establish the existence of a compact global random attractor. The existence of a random absorbing set is first discussed for the systems and then an estimate on the solutions is derived when the time is large enough, which ensures the asymptotic compactness of solutions. Finally, we establish the existence of the global attractor in <i>L</i>²(<i>D</i>)&#215;<i>L</i>²(<i>D</i>).