p-Laplacian方程在依赖时间赋范空间中全局吸引子的存在性

Existence of Global Attractors for p-Laplacian Equations in Time-Dependent Normed Spaces

对非自治p-Laplacian系统的长时间动力学行为进行了研究.在带参变量t的有界赋范空间中,给出拉回吸收集、全局吸引子和过程的概念.利用时间全局吸引子理论,说明过程在拉回意义下吸收集是存在的.在正则性更高的空间中过程是有界的,利用Sobolev嵌入定理,说明过程是拉回渐近紧的,进而得到结论:依赖于时间t的全局吸引子是存在的.

The long time dynamical behavior of the non-autonomous p-Laplacian systems was studied. In bound normed space with parameter t, the concepts of pullback absorbing set and global attractor and process were given. Based on the recent theory of time-dependent global attractors, the process had absorbing sets in the sense of pullback. In the higher regular space, the process was bounded. Using the Sobolev embedding theory, the process was pullback asymptotically compactness. It draws the conclusion that the global attractor which depends on the parameter t is existed.