The Asymptotic Theory For Two Dissipative Infinity Dynamic Systems

In this paper, we study the asymptotic theory of two typical dissipative infinity dynamic systems in mathematics and physics. In the second chapter, the KDV type equation on unbounded domain is considered. Applying with the method of decomposing operator and the theory of constructing some compact operator in weighted space, the existence of exponential attractor is obtained. In the third chapter, the non-autonomous Schr?dinger-KDV type equations are considered. The existence of the uniform attractor of the system and the estimate of the uniform attractor's Hausdorff dimension are obtained.