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

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.