On The Existence Of Uniform Pullback Attractors For Nonautonomous Dynamical Systems

In this master's dissertation, we mainly consider the existence of uniform pullback attractors for nonautonomous infinite dimensional dynamical systems. As the symbol space is not a compact set, and the union of all the sections is not compact, we give a new sufficient and necessary condition to verify the existence of uniform pullback attractors. And the paper is organized as follows:This paper consists of four chapters.In the first chapter, we introduce the background of infinite dimensional dynamical systems and briefly show the development and research for global attractors, uniform attractors and pullback attractors in autonomous and nonautonomous case respectively. Moreover, we introduce the main problem and ideas discussed in this paper.In the second chapter, some preliminary results and definitions are presented.In the third chapter, we firstly introduce the concept of uniform pullback attractor, and the previous result about the existence of uniform pullback attractors. Then we give the concept of uniform pullbackω—limit compact and the method to verify it. So, we obtain a new sufficient and necessary condition to verify the existence of uniform pullback attractor. It is worth to point out that the noncompactness of symbol space and the union of all sections in our case.In the fourth chapter, we discuss the relationship of several kinds of attrac-tors, and prospect the future of the problem studied in this paper.