Uniform Exponential Attractors for Second Order Non-autonomous Lattice Dynamical Systems  

作　　者：Xiao-peng ZHOU Fu-qi YIN Sheng-fan ZHOU 

机构地区：[1]School of Mathematics and Computational Science, Xiangtan University [2]Department of Mathematics, Zhejiang Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2017年第3期587-606,共20页应用数学学报（英文版）

基　　金：supported by Hunan Provincial Natural Science Foundation of China(No.2015JJ2144);National Natural Science Foundation of China(No.11671343 and No.11171280);the General Project of The Education Department of Hunan Province(No.12C0408);Zhejiang Natural Science Foundation(No.LY14A010012)

摘　　要：In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, a-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, a-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.

关 键 词：uniform exponential attractor quasiperiodic symbols a family of processes squeezing property lattice dynamical systems 

分 类 号：O19[理学—数学]