一类Ginzburg-Landau方程的动力学行为研究

发布时间：2018-09-05 05:47

【摘要】：本文主要讨论了一类Ginzburg-Landau方程的动力学行为问题.首先用(G'/G)展开法对Ginzburg-Landau方程进行了求解;接着又借助拉回条件C讨论了广义Ginzburg-Landau方程在L~2(Ω)空间中拉回吸引子的存在性,同时证明了3维空间中非线性的Ginzburg-Landau方程的拉回吸引子,最后讨论了复系数的Ginzburg-Landau方程的拉回吸引子的存在性.论文包括以下四个部分:第一部分介绍无穷维动力系统的发展历程,Ginzburg-Landau方程和拉回吸引子的概念以及国内外研究背景与研究现状;第二部分给出本文所需的基本概念和定理.比如常用不等式和函数空间,拉回吸引子的相关性质和判定定理;第三部分讨论了二维常系数非线性Ginzburg-Landau方程解的存在性;第四部分证明了广义Ginzburg-Landau方程拉回吸引子的存在性,通过解的存在性证明其存在拉回吸收集,并借助拉回条件C,证明该方程在L~2(Ω)中存在拉回D-吸引子;然后讨论了3维空间中非线性的Ginzburg-Landau方程的拉回吸引子.最后,借助不等式讨论了复系数的Ginzburg-Landau方程的拉回吸引子的存在性.
[Abstract]:In this paper, the dynamic behavior of a class of Ginzburg-Landau equations is discussed. Firstly, the Ginzburg-Landau equation is solved by using the (G / G) expansion method, and then the existence of the pull back attractor of the generalized Ginzburg-Landau equation in the L ~ (2 (惟) space is discussed by means of the pullback condition C, and the pullback attractor of the nonlinear Ginzburg-Landau equation in the three-dimensional space is proved. Finally, the existence of the pull-back attractor for the Ginzburg-Landau equation with complex coefficients is discussed. The thesis includes four parts as follows: the first part introduces the development course of infinite dimensional dynamical system: the concept of Ginzburg-Landau equation and pull back attractor, the research background and present situation at home and abroad; the second part gives the basic concepts and theorems needed in this paper. In the third part, we discuss the existence of solutions for two-dimensional nonlinear Ginzburg-Landau equations with constant coefficients, and in the fourth part, we prove the existence of pull attractors for generalized Ginzburg-Landau equations. By the existence of the solution, the existence of the pullback absorption set is proved, and the existence of the pullback D- attractor in the L ~ (2 (惟) is proved by means of the pullback condition C, and then the pullback attractor of the nonlinear Ginzburg-Landau equation in three dimensional space is discussed. Finally, the existence of the pull attractor for the Ginzburg-Landau equation with complex coefficients is discussed by means of inequalities.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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