Asymptotic Behavior Of Two Kinds Of Nonautonomous Lattice Systems

In this dissertation, we study the pullback exponential attractors of the non-autonomous Long Wave-Short Wave Resonance Equation, also consider the ex-istence and upper semi-continuity of kernel sections of the lattice system cor-responding to the FitzHugh-Nagumo Equation in the weighted space l?2×l?2 The pullback exponential attractors, with positive invariant sets and finite frac-tal dimensions, contain the pullback attractors, and the exponentially attract all bounded sets. The pullback exponential attractor is an important concept to describe the dynamic behavior of infinite dimensional system. The kernel section is another important concept used to describe the long-term behavior of a non-autonomous dynamical system. At the same time, we introduced the main work of this article.In chapter 1, we introduced the development history and the present situation of the infinite dimensional lattice dynamical system, at the same time, gave the concept of pullback exponential attractors and kernel sections, and commonly used definitions and inequalities. At last we introduced the main work of this dissertation.In chapter 2, we considered the asymptotic behavior of the solution of the lattice system corresponding to the Long Wave-Short Wave Resonance Equation,and obtained the conclusion that the above lattice system possess pullback expo-nential attractors.In chapter 3, we considered the asymptotic behavior of the solution of the lattice system corresponding to the FitzHugh-Nagumo Equation in the weighted space l?2×l?2 and obtained the conclusion that the above lattice system about the kernel section and its semi-continuity.In chapter 4, we have made a summary and prospect of this dissertation.