Uniform exponential attractors for second order non-autonomous lattice dynamical systems

作者：Zhou, Xiao-peng; Yin, Fu-qi^*; Zhou, Sheng-fan

来源：Acta Mathematicae Applicatae Sinica-English Series, 2017, 33(3): 587-606.

DOI：10.1007/s10255-017-0684-z

• uniform exponential attractor
• quasiperiodic symbols
• a family of processes
• squeezing property
• lattice dynamical systems

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, alpha-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.

• 出版日期2017-7
• 单位浙江师范大学; 湘潭大学