两类非自治格点系统的渐近行为

发布时间：2018-05-01 05:36

本文选题：拉回指数吸引子 + 核截面　；参考：《湘潭大学》2017年硕士论文

【摘要】：本学位论文研究了非自治长短波谐振方程对应格点系统的拉回指数吸引子和FitzHug- Ngumo方程对应的格点系统在加权空间lσ2 × lσ2中的核截面的存在性及其上半连续性.拉回指数吸引子包含了拉回吸引子,且指数吸引所有有界集,具有有限分形维数的正向不变集,是用来描述无穷维格点系统动力学行为的一个重要概念;核截面是另一个用来描述非自治动力系统长时间行为的重要概念.本文内容安排如下:在第一章中,我们简述了无穷维动力系统的发展历史及现状,并给出了拉回指数吸引子,核截面的概念,以及本文中用到的定义和不等式,同时介绍了本文的主要工作.在第二章中,我们考虑了长短波谐振方程所对应的格点系统的解的渐近行为,得到了该系统拉回指数吸引子的存在性的结论.在第三章中,我们考虑了FitzHugh-Nag umo方程对应的格点系统在加权空间lσ2 × lσ2中解的渐近行为,得到了该系统核截面的存在性及其上半连续性的结论.在第四章中,我们对本文进行了总结与展望.
[Abstract]:In this dissertation, we study the existence and upper semicontinuity of the lattice system corresponding to the nonautonomous long-short wave resonance equation in the weighted space l 蟽 2 脳 l 蟽 2 and the lattice system corresponding to the Fitz Hug- Ngumo equation. The pullback exponential attractor contains pull attractor and exponentially attracts all bounded sets and positive invariant sets with finite fractal dimension. It is an important concept used to describe the dynamical behavior of infinite dimensional lattice point systems. Nuclear cross section is another important concept used to describe the long-term behavior of non-autonomous dynamical systems. The contents of this paper are as follows: in the first chapter, we briefly describe the development history and present situation of infinite dimensional dynamical system, and give the concepts of pull back exponential attractor, nuclear cross section, definitions and inequalities used in this paper. At the same time, the main work of this paper is introduced. In the second chapter, we consider the asymptotic behavior of the solution of the latticed system corresponding to the long and short wave resonance equation, and obtain the existence of the pull back exponential attractor of the system. In chapter 3, we consider the asymptotic behavior of the solution of the lattice system corresponding to the FitzHugh-Nag umo equation in the weighted space l 蟽 2 脳 l 蟽 2, and obtain the existence of the kernel cross section of the system and its upper semi-continuity. In the fourth chapter, we summarize and look forward to this paper.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19

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