Uniform exponential attractors for second order non-autonomous lattice dynamical systems |
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Authors: | Xiao-peng?Zhou Email author" target="_blank">Fu-qi?YinEmail author Sheng-fan?Zhou |
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Institution: | 1.School of Mathematics and Computational Science,Xiangtan University,Xiangtan Hunan,China;2.Department of Mathematics,Zhejiang Normal University,Jinhua Zhejiang,China |
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Abstract: | 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, α-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. |
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