线性耦合热方程的唯一连续性

发布时间：2018-07-03 18:02

本文选题：耦合热方程 + 唯一连续性　；参考：《河南师范大学》2017年硕士论文

【摘要】：本文主要研究有界凸区域Ω上的线性耦合热方程的唯一连续性质.其中耦合热方程满足齐次狄利克雷边界条件,并且方程的系数和时间有关.本文分为三章,其中:第一章为绪论部分,主要分为两节,先介绍了关于偏微分方程的唯一连续性的研究现状,并且给出本文所研究的热方程及其满足的条件.然后,将我们的结果以两个不等式的形式给出:以及第二章首先引入函数Gλ(x,t),Hλ(t),Dλ(t)和频率函数Nλ(t),并研究它们的性质.最后利用频率函数法给出定理1.1和定理1.2的详细证明.从主要定理所得到的不等式不难看出:1.如果在一个小的区域ω上,y(x,T)= z(x,T)=0,则在一个较大的区域Ω上有,y(x,T)=z(x,T)= 0.2.如果在一个小的区域ω上,y(·,T)= z(·,:T)= 0,则在一个较大的区域Ω(0,T)上有,y(·,·)=z(·,·)= 0.第三章主要是对本文的内容做一个回顾与总结.本文建立了线性耦合热方程的解的唯一连续性定理,并且给出了详细的证明.利用我们的结果,可以对更多类型的偏微分方程的解的唯一连续性质来做出一个具体的定量估计,甚至可以将我们的结论用于控制理论的研究.
[Abstract]:In this paper, we study the unique continuity of linear coupled heat equations on bounded convex domain 惟. The coupled heat equation satisfies the homogeneous Delikley boundary condition and the coefficient of the equation is time-dependent. This paper is divided into three chapters: the first chapter is the introduction, which is mainly divided into two sections. Firstly, we introduce the research status of the unique continuity of partial differential equations, and give the heat equations studied in this paper and their satisfying conditions. Then, we give our results in the form of two inequalities: in the second chapter, we introduce the function G 位 (XT) H 位 (t) D 位 (t) and the frequency function N 位 (t), and study their properties. Finally, the detailed proofs of Theorem 1.1 and Theorem 1.2 are given by the method of frequency function. The inequality obtained from the main theorem is not difficult to see: 1. If we have y (XT) = z (XT) 0 on a small region 蠅, then we have y (XT) z (XT) = 0.2 on a larger region 惟. If y (T) = z (n: t) = 0 on a small region 蠅, then there is y (,) z (,) = 0 on a larger region 惟 (0T). The third chapter is a review and summary of the content of this paper. In this paper, the unique continuity theorem for the solution of the linear coupled heat equation is established, and the detailed proof is given. By using our results, we can make a specific quantitative estimate of the unique continuity of solutions of more types of partial differential equations, and even apply our conclusions to the study of control theory.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.2

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