非自治微极流方程组在二维有界区域上的拉回渐近行为

发布时间：2019-01-06 05:09

【摘要】：非线性偏微分方程是基础数学与应用数学中的一个重要研究领域,与其他数学分支有广泛的联系,并且在自然科学与工程技术中有广泛的应用.非线性偏微分方程理论中主要的研究课题之一是揭示解的适定性和渐近行为.微极流方程组作为一类重要的非线性偏微分方程,它刻画了一类非牛顿流的运动,对于从事研究流体动力学问题和现象的工程师和科学家是非常重要的.本硕士论文主要研究在二维有界区域上非自治微极流方程组和含无穷时滞项时非自治微极流方程组解的适定性和拉回渐近行为.论文具体安排如下：第一章概述微极流方程组的物理背景和当前的研究情况以及本文所研究的问题.第二章研究二维有界区域上非自治微极流方程组解的拉回渐近行为.首先介绍该方程组解的整体适定性,然后证明拉回吸引子的存在性和正则性,最后证明拉回吸引子的缓增行为和H2有界性.第三章研究二维有界区域上含无穷时滞项时非自治微极流方程组解的整体适定性和拉回渐近行为.首先证明该方程组解的适定性,然后证明拉回吸引子的存在性.第四章论文小结与展望.
[Abstract]:Nonlinear partial differential equation is an important research field in basic mathematics and applied mathematics. It has extensive relations with other branches of mathematics and has been widely used in natural science and engineering technology. One of the main research topics in the theory of nonlinear partial differential equations is to reveal the fitness and asymptotic behavior of solutions. As an important class of nonlinear partial differential equations, the micropolar flow equations describe the motion of a class of non-Newtonian flows, which is very important for engineers and scientists engaged in the study of hydrodynamic problems and phenomena. In this thesis, we mainly study the solution of nonautonomous micropolar flow equations and nonautonomous micropolar flow equations with infinite delays in a two-dimensional bounded domain. The main contents of this paper are as follows: the first chapter summarizes the physical background of the micropolar flow equations, the current research situation and the problems studied in this paper. In chapter 2, we study the pullback asymptotic behavior of solutions of nonautonomous micropolar flow equations in two dimensional bounded domain. This paper first introduces the global adequacy of the solution of the system, then proves the existence and regularity of the pull back attractor, and finally proves the slow increasing behavior and H 2 boundedness of the pull back attractor. In chapter 3, we study the global fitness and pullback asymptotic behavior of solutions of nonautonomous micropolar flow equations with infinite delays in a two-dimensional bounded domain. First, we prove the adequacy of the solution of the system, and then prove the existence of the pull back attractor. The fourth chapter is the summary and prospect of the thesis.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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