DYNAMICS FOR A NON-AUTONOMOUS REACTION DIFFUSION MODEL WITH THE FRACTIONAL DIFFUSION

In this paper, we study the dynamics of a non-autonomous reaction diffusion model with the fractional diffusion on the whole space. We firstly prove the existence of a (L-2,L-2) pullback Du-attractor of this model. Then we show that the pullback Du-attractor attract the Du class (especially all L-2-bounded set) in L2+delta-norm for any delta is an element of[0,infinity). Moreover, the solution of the model is shown to be continuous in H-s with respect to initial data under a slightly stronger condition on external forcing term. As an application, we prove that the (L-2,L-2) pullback Du-attractor indeed attract the class of Du in H-s-norm, and thus the existence of a (L-2,H-s) pullback Du-attractor is obtained.