|本期目录/Table of Contents|

[1]徐 循.特征值及其在偏微分方程中的应用[J].绵阳师范学院学报,2018,(05):1-3,27.[doi:10.16276/j.cnki.cn51-1670/g.2018.05.001]
 XU Xun.Eigenvalue and its Application in Partial Differential Equation[J].Journal of Mianyang Normal University,2018,(05):1-3,27.[doi:10.16276/j.cnki.cn51-1670/g.2018.05.001]
点击复制

特征值及其在偏微分方程中的应用(PDF)
分享到:

《绵阳师范学院学报》[ISSN:1672-612X/CN:51-1670/G]

卷:
期数:
2018年05期
页码:
1-3,27
栏目:
数学与统计
出版日期:
2018-05-15

文章信息/Info

Title:
Eigenvalue and its Application in Partial Differential Equation
文章编号:
1672-612X(2018)05-0001-03
作者:
徐 循
湖北工业大学工程技术学院公共课部,湖北武汉 430068
Author(s):
XU Xun
Department of General Course, Hubei University of Technology Engineering and Technology College, Wuhan, Hubei 430068
关键词:
W120(Ω) 近似解 能量估计 弱解
Keywords:
the space of W120(Ω) approximate solution energy estimate weak solution
分类号:
O175
DOI:
10.16276/j.cnki.cn51-1670/g.2018.05.001
文献标志码:
A
摘要:
本文应用特征值及特征函数解决了一类二阶自共轭椭圆偏微分方程的边值问题.先求出算子A的特征向量{φk}k=1,然后在空间W1,20(Ω)上的规范正交系{φk}mk=1构成的有限维子空间中构造出方程的近似解,并通过能量估计定理将近似解取极限得到弱解,最后证明弱解的存在唯一性,从而得出弱解即是方程的通解.
Abstract:
This paper will apply the eigenvalues and eigenfunction to solve the boundary value problems of a class of second-order self-conjugate elliptic partial differential equation. First, it will figure out the eigenvectors {φk}k=1 of the operator A. Then, the approximate solution of the equation is constructed in the finite dimensional subspace formed by the canonical orthogonal system {φk}k=1 of the space of W1,20(Ω). And then it will obtain the approximate solution by the energy estimation theorem. Finally, the existence and uniqueness of the weak solution are proved. Consequently, it will get the conclusion that the general solution of the equation is the weak solution.

参考文献/References:

[1] Lawrence C.Evans.Partial Differential Equations[M].Graduate Studies in Mathematics,19.New York:American Mathematical Society,Province,RI,1998:349-358.
[2] 陈恕行.偏微分方程概论[M].北京:人民教育出版社,1981:17.
[3] 陆文端.微分方程中的变分方法[M].四川:四川大学出版社,1996:65.

相似文献/References:

备注/Memo

备注/Memo:
收稿日期:2017-12-05
作者简介:徐循(1986-),女,湖北宜城人,讲师,硕士,研究方向:偏微分方程
更新日期/Last Update: 2018-05-15