几种拉回吸引子的存在性与唯一性及其在p-Laplacian格点系统中的应用  

Existence and Uniqueness of Several Types of Pullback Attractors and Applications to Non-Autonomous p-Laplacian Lattice Systems

作　　者：李琳 杨袁 舒级 LI Lin;YANG Yuan;SHU Ji(Department of Primary Education, North Sichuan Preschool Educators College, Guangyuan Sichuan 628017, China;Department of Mathematical Foundations, Sichuan Tourism University, Chengdu 610100, China;School of Mathematical Science and V.C. and V.R. Key Lab, Sichuan Normal University, Chengdu 610068, China)

机构地区：[1]川北幼儿师范高等专科学校初等教育系,四川广元628017 [2]四川旅游学院数学基础部,成都610100 [3]四川师范大学数学科学学院&可视化计算与虚拟现实四川省重点实验室,成都610068

出　　处：《西南师范大学学报（自然科学版）》2021年第9期1-9,共9页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：四川省教育厅自然科学一般项目(17ZB0182);国家自然科学基金项目(11871138);四川旅游学院科研创新团队项目(20SCTUTY01).

摘　　要：推广了拉回吸引子的定义,提出了半一致紧的D拉回吸引子与半一致吸引的D拉回吸引子的概念且建立相应的抽象结果.这两个理论结果被应用于定义在无界整数集上的非自治p-Laplacian格点系统.证明了该系统在能量空间l^(2)中分别具有一个唯一的半一致紧的D拉回吸引子与一个唯一的半一致吸引的D拉回吸引子.此外,还研究了这些吸引子之间的结构与关系.In this paper, the definition of pullback attractors has been generalized, the concepts of semi-uniformly compact D-pullback attractors and semi-uniformly attracting D-pullback attractors been introduced, and corresponding abstract results been established. The two abstract results have been applied to a non-autonomous p-Laplacian lattice system defined on the integer set. It shows that the system has a unique semi-uniformly compact D-pullback attractor and a unique semi-uniformly attracting D-pullback attractor in the energy space l^(2). In addition, the relationship and structure of those attractors have also been investigated. The main difficulties is to overcome the non-compactness of embeddings in infinite lattice systems and the nonlinearity of the discrete p-Laplace operator for p>2.

关 键 词：p-Laplacian格点系统 非自治动力系统 半一致紧的D拉回吸引子 半一致吸引的D拉回吸引子 

分 类 号：O211.4[理学—概率论与数理统计]