The Pullback Attractor Of A Class Of Second-order Nonlinear Equations

As the field of physics, fluid field natural disciplines began to appear more and more new phenomenon, numbers of new problems need to solve, the study of infinite dimensional dynamical systems get widespread concern and attention. The pullback attractor of non autonomous is an important theoretical tool for infinite dimensional dynamical system which with "pullback dissipative". Pullback attractor theory subject has been touted scholars, and corresponding theoretical system still imperfect.Proving that the existence of the pullback attractor is required to verify the three properties of the pull back dissipation, the co-loop continuity and the asymptotic compactness. In the third and fourth chapters, the three properties are verified in the bounded and unbounded domains. When the existence of the attractors in a bounded domain is discussed, the method of verifying compactness is mainly based on the recent comparison of the new theory (D-pullback(C)) and the traditional Sobolev compact embedding theorem. The existence result of a relatively efficient attractor is obtained. Because the embedding is no longer tight when we prove existence of pullback attractors on the unbounded domain, we use segmentation function method circumvents this difficulty, in the segmentation of bounded domain part combination of time with a compact embedding theorem and effectively to obtain the solution space compactness results.