The Attractors Of Several Classes Of Non-autonomous Dissipative Dynamical Systems

This thesis is devoted to the existence of kernel sections and unform attractorsfor several classes of non autonomous dissipative dynamical systems. The resultswe obtained improve the previous ones.In Chapter 1, we introduce the development of autonomous and non autonomousdissipative dynamical systems. Meanwhile, we summarize the main results of thethesis.In Chapter 2, the long time behavior of three non autonomous evolution equations in unbounded domains is dealt with. First, we prove the existence of kernelsections for a non classical reaction diffusion equation by the method of energy equation. Then we study the existence of kernel sections for BBM equation and partlydissipative reaction diffusion equation by applying some technique of solution decomposition.In Chapter 3, we consider a non autonomous non local reaction diffusion equation with delay in R~N, and prove the existence of kernel sections in weighted Sobolevspace.Chapter 4 deals with a class of non autonomous non local parabolic equationswith delays. The existence and regularity of kernel sections are obtained.In Chapter 5, we study a class of non autonomous parabolic equations withdelays and prove the existence of uniform attractors for the family of processesgenerated by weak and strong solutions.In Chapter 6, by applying the theory of multi valued process, we prove theexistence of unform attractor for a partial functional di?erential equation with discrete state dependent delay. As a corollary, we get the unique periodic and almostperiodic solutions.In the last Chapter, a partial functional di?erential equation(whose linear partis not densely defined but satisfies Hille Yosida condition) is considered. The existence of uniform attractor is proved. As a corollary, the existence of periodic andalmost periodic solutions is obtained.