本文選題：拉回指數(shù)吸引子 + 核截面��； 參考：《湘潭大學(xué)》2017年碩士論文

【摘要】：本學(xué)位論文研究了非自治長短波諧振方程對應(yīng)格點(diǎn)系統(tǒng)的拉回指數(shù)吸引子和FitzHug- Ngumo方程對應(yīng)的格點(diǎn)系統(tǒng)在加權(quán)空間lσ2 × lσ2中的核截面的存在性及其上半連續(xù)性.拉回指數(shù)吸引子包含了拉回吸引子,且指數(shù)吸引所有有界集,具有有限分形維數(shù)的正向不變集,是用來描述無窮維格點(diǎn)系統(tǒng)動(dòng)力學(xué)行為的一個(gè)重要概念;核截面是另一個(gè)用來描述非自治動(dòng)力系統(tǒng)長時(shí)間行為的重要概念.本文內(nèi)容安排如下:在第一章中,我們簡述了無窮維動(dòng)力系統(tǒng)的發(fā)展歷史及現(xiàn)狀,并給出了拉回指數(shù)吸引子,核截面的概念,以及本文中用到的定義和不等式,同時(shí)介紹了本文的主要工作.在第二章中,我們考慮了長短波諧振方程所對應(yīng)的格點(diǎn)系統(tǒng)的解的漸近行為,得到了該系統(tǒng)拉回指數(shù)吸引子的存在性的結(jié)論.在第三章中,我們考慮了FitzHugh-Nag umo方程對應(yīng)的格點(diǎn)系統(tǒng)在加權(quán)空間lσ2 × lσ2中解的漸近行為,得到了該系統(tǒng)核截面的存在性及其上半連續(xù)性的結(jié)論.在第四章中,我們對本文進(jìn)行了總結(jié)與展望.
[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.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O19

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本文編號：1827987