Pullback Exponential Attractions For Second Order Lattice Systems With Time-dependent Coupled Coefficients

The main content of this article is the existence of pullback exponential attractors for two kinds of second order lattice system with time-dependent coupled coefficients: j=-q in the space l2×l2and the weighted spaces lp2×lp2, respectively. Where for i€Z, ui∈R, are locally integrable in t, and λi, α are positive constants. Moreover, we obtain the upper bound of fractal dimension and attracting rate for the attractor. Pullback exponential attractors is a positive invariant set with finite fractal dimension, which contains pullback attractors and attract all bounded sets exponentially. It is a appropriate tool for the study of asymptotic behavior of non-autonomous dynamical systems.This paper consists of three chapters. The first chapter present the introduction including research background, research situation, some basic concept, symbols and com-monly used theorem that relate to the article. The second chapter deals with the existence of pullback exponential attractors for (1), and the dimension is estimated. In the last chapter we research the existence of pullback exponential attractors for (2), moreover, we obtain the estimation of fractal dimension.